so your keyboard is working and ableton is capable of receiving commands from your keyboard, correct? As in when you press a key/turn a knob the little yellow box in the top right lights up showing that ableton is receiving midi signal?
if it's working, and you're just looking to assign keys/knobs/pads (i believe those are all on the axiom), click the "MIDI" button at the top right of the screen (everything will turn blue), then click on the parameter (IE volume, pan, etc) you want to control, then just turn whatever knob (or press whatever key or pad) on your axiom that you want to control the parameter, and it will automatically assign the physical knob to the parameter. If this doesn't happen, you don't have your axiom hooked up right, and you might need to download drivers from m-audio.
the knobs are the easiest, i dunno if the pads on your axiom are the same as the buttons on my keystation pro, but if they are you might have to set the min/max parameters. if you plug it into a drum machine and it works then you're good and don't have to worry about it.
i don't know exactly what you're looking for, and i don't come around much so pm'ing isn't gonna work, so i'm trying to do my share to help all at once.
if you simply want sound to come out of an instrument, you have to either click the little rectangle with the circle in it (to the far right of the track in each track channel), or click"In" on the track channel (as opposed to "Auto" or "Off"). If you have the track you want sound to come out of set to "Auto" then no sound will play when you hit a key.
if you're looking to route seperate midi channels within ableton, you first need to figure out how to switch between midi channels (there are 16 of them typically) and then you can assign different instruments to different channels and have all kinds of shit pre-assigned to your keys when you open the program up (IE channel 1 to the mixer, 2 and 3 to different synths, 4 to the sampler, etc).go to the Arrange view and the the "Input" section of track will have a dropdown with a specific channel you can assign it to.
good luck! (and go to m-audio.com and get manuals/drivers)