I'm assuming you can already sing satisfactorily when you're doing nothing else. Now you just need to combine that "talent" (how ever much you may have) with drumming. I'm also assuming you're a competent drummer.
If you can't pick out a drum part by ear you're going to want a book of applicable drum tabs. You'll also need the recorded version of the song you want to learn if it's not an original song of yours.
Step 1: Learn Your Part
My drum teacher once told me, "If you can't carry on a coherent conversation while playing, you need to practice more." This is especially true of singing while you play. If you can't talk to someone without screwing up, you won't be able to sing without screwing up.
So go practice some more.
Step 2: Learn the Words
Hold your breath, and see how long you can hold it while just sitting in your computer chair. Now take another breath and see how long you can hold it while pacing the room. See, that's why breathing is crucial to singing while exerting yourself at the drumset.
If you are at all within danger of running out of air at any point in the song, you need to find a spot to take a breath in that passage. Breaths should be quick and noiseless, through your mouth, especially if you're cursed with hayfever like me. Take a breath at natural breakpoints in the music, not in the middle of a (breath) sentence. See how that doens't work? Think of Malcom's friend in the wheelchair from Malcom in the Middle. Don't breathe like him while you're singing.
Got plenty of air all through the song? Good, now combine it with drumming.
Step 3: Begin to Add in the Words
That's right, I said fail. The first time you try it, you'll get something wrong. Maybe a word, maybe a breath, maybe a note or three. Try, try again. Maybe you'll sound like you're 14 again, with your voice cracking all over the place. Maybe you'll be doing great and then your brain locks up and you have a spasm all over the drumset the sounds awful and makes you loose your place. Put some WD-40 on your brain and when it's un-seized, try again.
Don't try and do it all at once. I'm going to use When You Were Young by The Killers as an example, since that's the song I first had to learn how to do this on. If you've got to learn The Cisco Kid, it'll be tougher.
Now let me say that instead of playing straight eighths in my foot, I would swing it a little, playing it as sixteenth note doubles. That doesn't make things easier at all. At first I'd neglect the foot during the second verse (the part that we decided we'd all harmonize on), but I eventually got the foot to the point where I wouldn't have to move it back to straight 8ths or otherwise back off from what I was playing.
The "When you... were young" part, which is not perfectly timed with the rest of everything but instead a little syncopated is a tough part to get. I skipped it the first few times through and just held the beat so that I could get the rest right. Take things half a verse at a time.
Step 4: Figure Out What You're Doing Wrong
You back? Okay, now things have had a chance to sink in and you're ready to work some more. I learned this from my guitar teacher, but it applies to all instruments: when something turns into a train wreck, it's probably not right where the wreck hapened that's the problem. It's probably about a half a mile up the track. Fix the part right before you Phail epically, and you'll have elimainated the failure point. No more musical train wreck.
Step 5: How Do You Play?
Now don't go changing your style. That's another variable you don't need. Just learn to lift your leg differently while you play heel up. Don't just wrench it up with your abs. Anticipate it (go back to step one and practice your whole drum part this way now) and don't wrench you leg up with your abs all of a sudden. Rock it up more smoothly without tensing your abs. Tensing your core muscles will wreck your singing.
That's right, drumming should always be relaxed. Even if you're playing an energetic peice, you shouldn't be panicing or racing yourself or anything like that. You should own that part, know it inside and out, and be ready. You know that. Drumming while you're tense about something is like trying to drive by looking right over the hood ornament at the road two feet in front of your car. No control, no time to react, no breathing space.
Breathe. You'll be fine.
Step 6: Other Ways to Wreck Your Singing
That's right, flow. You've probably been told how to hold your sticks and all that, but I'll reiterate. You want to be playing from the hand and the wrist, playing power passages from the elbow only if we absolutely must for volume.
Don't worry if my hand mysteriously changes color or looks like I airbrushed it on. That would appear to be a side effect of taking the pistures with my Windows Media Player visualizer as the background. I am not actually in a state of chromic flux.
Step 7: Practice, Practice, Practice
I say perfectly, but you won't be. I know it. You know it. We all know it. You have to also practice enough that you can roll with mistakes and make it still seem seamless, whether it was your mistake or someone else's that caused you to have to do damage control mode.
Sleep on it. Don't practice it or learn this all in one day. Do it over several days and sleep on it. Trust me, you'll have a couple fo drum-related dreams one night. That's just your brain learning it backwards and forwards, inside and out. Learning something over several days and sleeping on it is the best way to make somehing second nature. Do it.
Don't forget to play it with the rest of the band, too, and not just on concert day! That's a bunch more variables to throw a wrench in the works.