DIY Dungeons and Dragons

I actually got into DnD before I got into Warhammer. I got away really cheap, because everything I've used to play was DIY.

Abbreviations.
DIY = Do It Yourself. Though if you hadn't known that, you probably wouldn't be reading this.
DnD = Dungeons and Dragons, the game we're playing here.
DM = Dungeon Master, the person who narrates the events and controls the monsters. If you're reading this, it's probably you.
WotC = Wizards of the Coast, the company that makes DnD. Keep up the great work guys! Disclaimer in the footer of the page.

Things needed to play DnD (as a DM):

1. Rulebooks
2. Dice
3. Maps
4. Figurines (miniatures)
5. Character sheets (optional)
6. Spell cards (optional)
7. DM screen (optional)
8. Background sounds and music (optional)
9. An adventure
10. Players 

No. 1 Rulebooks

First things first, there's no way around this. There are rulebooks, and that's that.

No. 2 Dice

Dice are cheap and are an integral part of the physical "feel" of the game. You should definitely use physical dice!
However, if you don't like or really can't afford them, you can download a dice roller app for your smartphone. There are graphical apps where you shake your phone and it shows dice being rolled; there are simple apps where you click a button and it shows the numeric result; your choice. An advantage here (if you use an advanced app) is that you can register certain rolls, such as "1d20+5" and name it "History check" or "2d6+3" and name it "Weapon damage".

No. 3 Maps

The first piece of DIY! Not exactly inexpensive, but here goes:
Step 1.
Search the internet for "dnd maps","dungeon tiles" and so on. There's a plethora of free maps available for download. You might have to work a bit on some of them (e.g. make sure that, when printed, the squares are 1 inch high/wide). You can find PDF editors for free on the internet, that you can use to make measurements and realign an otherwise un-editable document.

There's also the chance you can find freely available complete adventures, made by WotC, with attached maps. Here's one I've began with two separate parties, though we never finished it. If you're one of my players, don't click this! Keep on the Shadowfell This is the best option here, as you can be sure that the maps are high quality and of the right size.
Step 2.
Get a color printer and print the maps. This is usually cheaper if you don't use your own, as they would consume a lot of ink.
Step 3.
Maps (especially complete maps, such as those attached to free adventures) are huge. As in 6 A4 pages huge. Here's some ways that I tried to assemble them:

This is my first try. I tried to assemble all the fragments into a single piece of paper. Didn't work out very well, as the pieces on the left end (the one where they aren't glued together, so that I can fold them up) are not completely aligned. Good enough though.

This is how the other side looks like. (If you look closely, you can see the sheet of glass placed over the map - that's explained below.)

For this map, I only glued 2 sheets together each, so that 4 separate pieces form the entire map:

Of course playing with that and dragging figurines on it would be a nightmare. So add a sheet of glass (or transparent plastic, plexi, whatever):

This keep the map in place by adding weight and preventing dragging. If you have an erasable marker, you can also draw area effects on it. It also protects the map from spilled beverages.

No. 4 Figurines (miniatures)

As I've said in previous posts (and I can't stress this enough), miniatures are expensive. Furthermore, miniatures intended for RPGs are even more expensive than wargaming ones, since we're talking about detailed, individual characters, and not 10-20 almost identical models. There are still ways to save money (check out my miniature trade section). You can also try out one of the DnD-themed boardgames by WotC, they contain a fair amount of plastic miniatures. I've seen some of these at the store, but, as I wanted to play actual DnD (and these are still expensive), I didn't buy any. Check out Dungeons & Dragons: Wrath of Ashardalon at BoardGameGeek.
Another issue besides price is the huge variety of available miniatures. As an aspiring Dungeon Master, I looked up several adventures to play, and the number and type of creatures you can meet even in low level adventures is... daunting. You can buy an army's worth of kobolds, goblins, gnolls and orcs, and you may still find yourself needing just that one more goblin crossbowman. Or even worse, never using what you have.
Alternative 1 Buy some miniatures and use them as proxies.
Sure, you can pretend that all those kobold slingers are actually goblin archers. Your players might even get used to it. But pretending that that orc axeman is a halfling bartender is lame. You're better off using tokens.
Alternative 2.1 Arbitrary tokens
That coin is the halfling bartender. End of story.
Alternative 2.2 "Real" tokens
I'm talking about flat, coin-like pieces of paper with the monster drawn/printed on it. You can find some on the internet, or even produce them yourself using custom images and a photo-editing software (MS Paint works well). Just print them and cut them out. For extra durability, glue the printed-on paper on cardboard.

These are great since they're inexpensive (printing costs) and graphical enough (actual monster shown). Your players might also be used to using them, since many boardgames rely on such tokens.
 However, for someone who has already played with miniatures, they feel too 2D.
Alternative 3 3D paper cutouts
This is the option that I've actually settled at. There's more work here than with tokens, but it's greatly satisfying to push around your miniature-like cutouts on the board.

Producing 3D cutouts

Step 1. Produce some blueprints
Search the internet for "free paper cutouts"; here's a collection of links to get you started.
There's a huge variety available. However, if one your players happens to choose that one race/class combination that you haven't found anywhere, feel free to produce your own.
Step 2. Print them
If you want to save on printing costs, you can produce 1-sided "figurines". However, I don't feel like turning them constantly around so that everybody gets to see what's on them, so I've printed them double faced. You'll see what I'm talking about immediately. This is easy to do at home with your own printer.
Step 3. Cut them out
Make sure you make gluing easy. So if you've placed the picture of the monster two times next to each other, cut them out together and fold the cutout in half, so that each face presents the monster.
Step 4. Glue them
This should produce appropriate sized, flat, double-faced cutouts.
Step 5. Produce bases for them
Basically repeat steps 1-5 for the bases. Look for "cutout base for miniatures" on the internet.

You only need a limited amount of bases (you won't have more than 20 monsters on the map at once).

This gives you an unlimited amount of inexpensive figurines. Being flat pieces of paper, they are also easy to store. i.e. a butter box holds around 100 such cutouts and it isn't even half-filled. You can see them in action in the pictures at the bottom of the post!

Comment: We're done with the required material part. You can skip to step 9 if you don't feel like doing anything more. However, I felt that the following small items greatly enhance gaming experience.

No. 5 Character sheets (optional)

Instead of scrawling down everything by hand on sheets of white paper, use the character sheets provided by the rulebook. Print them out in black-and-white. You can fill them out for each character before printing, and use a pencil for additions, or just print them out blank and fill them by hand. In either case, it adds a personal touch to put in a picture/portrait for the character. Even in black-and-white, they give the player a sense of how their avatar looks like.

No. 6  Spell cards (optional)

You can note down the powers on the character sheets, but you will either write in a very small font (hard to read) or just note the powers' names (everybody needs to keep a rulebook open). You will also need to mark, un-mark and re-mark used up encounter and daily powers.
Use spells cards instead. The WotC website provides a spell card generator customized for DnD, but it requires a paid subscription for their service (which, by the way, offers lots of awesome stuff). Since we're taking the cheap route here, use a generic spell card generator (e.g. http://tools.omnichron.net/dnd/pow.html) and fill out the cards by hand. Print them out in black-and-white, then use colored markers to color-code them (to keep inline with the rulebook, green for daily, red for encounter, grey for daily powers).
Not only will spell cards allow a player to spread out the list of available powers on the table (instead of flicking back-and-forth in the rulebook), they also provide an easy way of tracking used-up powers: flip the spell card face down!

No. 7  DM screen (optional)

I've read some pros and cons about the DM screen, and I've decided to use it. Since we're going cheap, I've made my own DM screen using two pizza boxes. The white side is facing the players (if you can print some pictures/illustrations and glue them on it, even better) and the colored side is facing the DM. Over that I glued white paper, on which I printed/wrote by hand useful things such as standard difficulty classes, actions that can be taken during a round, prices etc. This greatly speeds up the game when you have to take a quick decision on the spot.
It's a great front behind which you can roll dice, prepare monsters for the next encounter, hide a notebook and scribble down the going of the battle e.g. initiative order, monster health left etc.
You can also use it to show initiative order to the players. Use pieces of white paper bent in the middle and place them on top of your DM screen. For the players, write the character's name on both sides (so that both you and them can see who's coming up). For the monsters, write the monster's name on you side of the paper only (so the players will know a monster is coming up, but won't know which one). Then go left-to-right (or right-to-left, whatever). Rearrange at the start of each battle (and watch the expression on the players' face as you put up 4-5 blank pieces of paper :D).

No. 8  Background sounds and music (optional)

Background sounds work wonderfully for setting the atmosphere. Use a free website (e.g. http://naturesoundsfor.me/) or smartphone app to play any number of nature sounds when going through a forest, crossing a river etc. You might even find background sounds for sitting in a tavern or fighting. Just don't forget to change the sounds along with the scenery!
Alternatively, play some inspiring music. Get your hands on soundtracks for suitably heroic movies and games (fantasy RPGs work best) or use this free website (https://www.radiorivendell.com/)

No. 9 An adventure

As a new GM lacking experience, your best bet is to look for the free introductory adventures provided by WotC. These are great as they provide a complete story, full description of characters, locations, monsters, background events, as well as full description of encounters, monster actions, mechanics, traps etc. You will also find monster stats next to each encounter, so you don't have to keep flicking back-and-forth through rulebooks.
Once you have gained more experience, you can look for other adventures on the internet. There's a plethora of free fan-made stuff available. Some are even as (or almost as) complete as the ones made by WotC. The only drawback is that they're mostly for older editions. This is why you need the experience - to make the necessary adaptations. Don't forget to transplant all monsters, traps, characters etc to the current edition.
Here's a link to get you started.

No. 10 Players 

I can't help you with this one. You must gather your own!

Feel like playing yet? Here are some pictures of me and my friends playing with the accessories listed above to get you going.

After annihilating a large band of kobolds, the heroes rest around the magic circle in the shade of trees. From left to right: ranger, warden, bard, wizard, cleric.
Accessories: spell cards (printed black-and-white, painted over with colored markers), character sheets, pencils, dice.

A different band of adventurers take on the goblin overseer of the kobold bandits.The panther is a druid in animal form.

The DM's view: laptop (to keep track of the adventure), DM screen with cheat sheet on it, paper notes to track initiative. The DM screen also hides my notebook where I scribble down the flow of combat and monsters' health, whose blooded etc. and the next horde of monsters about to charge from the back of the cave.

 

 The party's first boss encounter is going badly. Two heroes are already down...

 

 ... but the goblin finally dies. The warden poses triumphantly on his corpse. Now, to haul their friends to the nearest temple for resurrection...

The fully restored party takes on the next challenge. Leave it to the minotaur to ignore all tactics and charge in!