This is kind of a general overview, the basic concepts are fairly simple. I looked at a lot of info out there before building my own, and I just kind of planned it as I built, it just takes a little creativity. Sorry to not include any links, just google it, I couldn't find the specific pages I used, but there is a community of people out there who do this stuff.
So an electronic drum set can run you back $600-3000+, sometimes without a module, my main reason for doing this was to save money bigtime. For comparison the cost for me was around $150-200 for all parts, then the module, so a total of at most $370, which as you drummers know is even cheaper than entry level acoustic sets! The most expensive item was the electric drum module or heart of it all which I will get to later. Heres a quick summary of my bill of major materials and costs:
-Drum pads -> 2 used toms 10" and 12" about 20$ each
-Cymbals -> plastic practice cymbals, $30 for a set
-Bass pedal/stands/mounting hardware -> came from existing acoustic set FREE
(note: I had these laying around, I would suggest being a bit creative about your solution if you dont own a drum set. I had first planned on using pvc or steel pipe, it would be much cheaper as a drum stand can run up to about 100$ for a simple studry one, Perl,Tama etc. The bass pedal might be the only thing you need to purchase, check for used hardware etc, or again, this is Instructables, your crafty people :-P).
-1/4" mono Wires (one per pad) & Electronic parts, $30-40
-Wood -> FREE (scavenged)
-Drum Module, $170 (ebay, "Alesis D4")
Basically I'm trying to convey how little money you would actually have to spend to have a working set minus the drum module. This set, after tuning the sensitivity of the pads (function of the drum module), gets about 4-5 levels of "volume" depending on the power of the hit. It's a great set for practice, and I wouldn't hesitate to play it live if I got the cash for a nice amp together...
Step 1: Pads 101
These are basically buzzers that can be bought at radio shack for about 2-3$ each. I believe they produce a signal when banged around that can be picked up by a drum module, translating the signal into a MIDI voice with the appropriate volume etc proportional to the impact. These are tiny flat discs when taken out of their casing, and are usually isolated from the impact of the stick by rubber/foam etc. Each disc has 2 wires, that you hook to a female 1/4" mono jack. The simplest pad would be say 2 cd-r's with the piezo glued in between them, covered by some material that your drum stick would be in contact with. Just make sure the piezo is attached to a rigid surface if you go the "sandwich" pad route, the vibrations travel better etc etc. Once you purchase these, you must "shell" them to get the actuall ceramic/metal disc out (see pics).
Most drum modules/pads work with 1/4" mono jacks, simple 2 conductor wires are used to link pads to module, the black wire (-) from the piezo goes to the tip of the plug, while the red wire is connected to the outer sheath. The cables I have are male ends, while the drum module and pads have female connectors. These are cheap and widely available at electronics stores as well.
I first just made the piezo circuit as a test, hooked it up to an amp, and gradually flicked the piezo while turning up the volume. Once I heard a sharp sound from the amp I knew I was in business (this means that the piezo was sending a signal when it was impacted, bumped etc. My 4 main drum pads are 2 toms that I stripped hardware from, and sliced in half (I built a jig for my tablesaw to rotate the drum while cutting, easier options exist :-P). I went with a "suspended bridge" to go across the center of the drum and hold the peizo, sandwiched in in foam, up against the drum head, (the foam just push the head up in the middle ever-so-slightly for contact). I used mesh heads, like screen door material, as the sound the head will produce is useless as the real sound comes from the drum module, plus this keeps it quiet. I wanted to do it this way to emulate the more expensive pads that allow you to use drum heads, the feel is just like a normal set!
Cymbals are much easier, get a flat disc/rigid surface, and glue/fasten the piezo right to it, hook it to a female jack, and there you go! For my hi-hat I had a practice pad laying around, I took it apart, added a cd-r with a piezo glued to it into the sandwich of foam under the drum head. Mousepad material is great for a surface if you desire to change the feel of your cymbals, or if you make flat pads, and skip the real drum look/feel. You could essentially glue 5 piezos+jacks to a board, cover them with mousepad material, and have a finger drum set, thats how easy this is!
If you look in the picture of the full set you can see inner rings in each drum, these are called RemO's and basically help to muffle vibrations. This keeps the reverberation of the drum head down so as to avoid "double-triggering" (basically 2 hits being registered when you only hit the pad once). Rigid sandwich pads probably won't suffer from this much if at all.
The object in the top of the picture of 4 items is a butane torch with a tip for soldering, which I should mentioned is involved in this project. Nothing really hard, just joining wires to wires and to the mono jacks.
Step 2: Bass Pedal/Hi-hat Trigger
For the pedal, I built a wooden frame that accepted a normal bass pedal, basically an L shape, with reinforcement. The piezo on this was sandwiched between some layers of mousepad and the assembly was placed at the right hieght to be struck by the beater when the pedal was pressed. You cant see in the picture, but the pedal clamps to the rounded bar on a simple door hinge that is in closed position and screwed onto the board on the underside.
The hi-hat trigger was a simple on off sustain footswitch for a keyboard I used to own. Anything that makes/breaks a connection can be used for my set as the module I have only supports an open or close hat, fancier modules can use a potentionmeter I believe for the open-ness of the hat.
Step 3: Drum Module
I'm sorry if I miseld you to think we would be building a module from scratch, or some other way to make sounds from the pads. I decided to buy a module as 170$ wasn't a huge deal if you look at other electronic sets prices, it was a worthwhile purchase for sure, and the only real big cost.
There are tons of modules out there for sale, most of them as far as I know function pretty much the same. Modules usually accept from 10-16 inputs which can be used for drums/cymbals/bass pedal. They have an assortment of sounds to program to each pad, and even the one I bought (Alesis D4) has very good adjustments for tuning the sensitivities of each pad (you could spend an hour per pad if you wanted). Modules can get pricey, and since I wasnt using professional pads, I just wanted the cheapest module, as many features might not have been available with the pads I built, rimshots etc. Though for a simple rim trigger I had at one point the rim of a frisbee with a piezo glued to it, mounted to the edge of my snare pad using the lugs that hold the metal rim on.
Once you have all that hooked together, the tuning begins. I basically tightened all the drum heads to my liking, and then went through each pad and changed settings on the module to give the pads the most dynamic output possible. This will differ with each drum module you buy so I cant give too much detail here without confusing people. I suggest searching around on google before you buy your drum module so you know what you're getting. There are forums where people have suggested which modules work best etc, this is your homework, do some research :-P
The Alesis D4 is perfect for my needs and also an entry level module, the more you spend, the more/better sounds, better hi hat features, you will get with a module. As far as connections the D4 gives me 2 sets of left and right 1/4" outputs (mono). There are people who have built their own midi triggers, basically a box with 1/4" inputs and midi output to take the signal from the pads and translate it for your computer. This way you set up the sounds on the computer itself, however then you need to haul a MIDI capable computer with you :-/.
Most of the time I use nice big headphones when I play, if you need to be heard, piping all the sound to one channel and into an amp is good, if you need stereo, 2 amps :-P.
Step 4: Final Comments
There is a wealth of information out there regarding projects like this, provided by both pros and other DIYers like ourselves. I couldn't have possibly put up all the info I found in this one instructable, but I believe I gave you enough info to get started and build a basic set.
Here's a video of the finished product, showing the sensitivity of the pads etc. I spent about 5-10 minutes tuning, with about 30 min I could have gotten perfect rolls on each pad instead of just the snare :-P. A good thing to keep in mind is that keeping the heads tighter (only an issue for the suspension method I used in my pads) allows for better piezo response and therefore more defined hit "signals" going to the module = fast drum rolls, good dynamic volume etc.
I'm no pro, in fact I dug this set up just to make the instructable, it was in storage for the summer... hopefully I'll get some more practice in. Being in apartments and dorms really took a blow at my drum skills but this set has only helped fill the niche! You do have to learn to play the set a bit differently, but it's almost a non-issue after the first 15-20 min. Tuning really helps this, gets rid of mis-read hits, etc, it can stop you up if you are playing normally but a pad doesn't trigger just right and you don't hear the sound you expected.
I will answer questions, send longer ones to firstname.lastname@example.org, good luck, and I hope some find this instructable worthwhile. Reading about the concepts and the ease of construction was very inspiring for me and I hope this helps others who are curious or stuck in my situation with housemates who enjoy silence ;-)