There are 2 drum machines in Ableton: Impulse, and Drum Rack. They are extremely similar, except in drum rack you can actually alter each specific drum track and drag effects into it, etc, and it is much easier to program drum rack onto midi pads or your keyboard (if you like to record them that way). Impulse operates by writing your drum patterns in.
For either Drum machine, all you have to do to get it up and running is to click on the drum machine and drag it into Ableton. You can drag it into session mode, or arrangement mode. Double clicking also works.
Now, once your drum machine is in Ableton, you can drag different sounds into it specific pads made for drums to go into. You can use Ableton's stock sounds, which are located in the instruments folder under Drum Rack. You can also use your own sounds, that you can get off of the internet. I personally am not into ableton's drum sounds so I use sounds from Deadmau5's sound library and a few other good ones. You can buy new sound packs on beatport or download them.
Personally, I like to pull in one kick, a couple of different hi hats, 3 snares, a percussion sound or 2, and a cymbal sound.
WRITING YOUR DRUM LINES:
If you want to write your drum lines by clicking them in (you can do this in both Impulse and Drum Rack), simply go to session mode, make sure your drum machine is record enabled, and double click on one of the tracks. this will enable you to write in midi. You can write in patterns in two ways: Double clicking midi notes in, and using the draw mode tool. You can double click midi notes into whatever pattern you want in the drum rack. You can use draw mode by clicking the pencil up top by the loop button or simply hit Command+B. In Draw mode, you can just simply single click in the pattern you want. If you want to write but don't like the grid you are in, (say you are writing in 8th notes and want to write in 32nds) you can right click and choose whichever subdivision of notes you want to work with which in this case is 32nds.
If you want to write your drum lines by physically recording them on midi pads or a keyboard (you can only do this in Drum Rack), find out what notes your midi pads are programmed to, and put your drums on those notes. Your midi pads should have all your drums on there. This might be a little confusing when you read it here from me, but let me know if you have any problems with this I can try to guide you through it. Next, click record and play your desired pattern.
When recording midi drums physically, it is easy to fuck up. When you are a little off time, you can simply get everything back on time by quantizing, or editing the midi notes with your draw tool or double clicking.
To Quantize, Simply click into where you can edit midi notes and hit command+A (Select all) and Command+U (Quantize). Remember, it will quantize to whatever subdivision you are working in. If you are working in 1/8th notes, it will quantize in 1/8th notes. If you want to quantize in 1/16th notes, just right click and click on 1/16th before quantizing.
Anyways, that's all I got for right now. Please let me know if you have any questions.