Here is a step-by-step guide:
I. Connect Resolume and Ableton
You need a MIDI loopback driver. On a Windows PC, MIDI Yoke is best (and free), IPMidi is also excellent and allows sending MIDI over network. On a Mac, either the app will appear as a MIDI endpoint, or you can use the IAC driver (which does the same as MIDI Yoke).
In the Ableton MIDI preferences, find your loopback (MIDI Yoke, IPMidi, IAC) and set track output to ON.
in Resolume, go to preferences and enable the same MIDI device. (Res 2.41 does by default, Res 3 you have to manually enable. Once done, setting is kept.)
I can highly recommend the IPMidi approach, keeping Ableton and Resolume on separate computers. If you are only using Ableton for MIDI, you do not need a very powerful computer at all.
II. Plan your MIDI layout
Important step, will make life much easier.
Here's how I do it:
1) Assign clips to be triggered by notes (white keys) in order, starting from Ableton octave 0 (= Resolume octave 2). So your clips will be triggered by C2, D2, E2, F2, G2, A2, B2, C3, D3, E3, etc...
2) Use MIDI channel 1 to trigger clips going to layer 1, MIDI channel 2 for layer 2, etc. I use MIDI channel 4 to trigger clips going to the active layer. I use MIDI channel 5 for other controls, such as switching decks, etc. Since Resolume potentially has many more layers, you might choose to use MIDI channels 11 and up for control, leaving 1-10 for use in clip triggering. I believe in Res 3 you would have to do this using the direct mapping, not the contextual mapping.
3) Assign a note for bypass layer and clear layer, for each layer and channel. You can use notes from Ableton octave -1 (Resolume octave 1). My notation will be note/channel. So for example, C1/1 bypasses layer 1, D1/1 clears layer 1, C1/2 bypasses layer2, D1/4 clears the active layer, etc.
4) Figure out what controller assignments you want to make. I tend to make these contextual mappings, eg. parameters 1-4 of the active layer.
Here's a picture of a simple Ableton set that does this: http://villamil.org/images/ableton_vj.jpg
III. Make MIDI assignments in Resolume
If you have a hardware MIDI controller, start Resolume, enable the MIDI controller for input, and learn all the MIDI notes. In Resolume 3, this is in the Mapping menu. In Resolume 2.41, this is in preferences dialog. Mostly you select a control, and then press the appropriate MIDI key.
If you don't have a hardware MIDI controller, open Ableton and Resolume at the same time. Make a MIDI track in Ableton. Set it to send MIDI to your loopback device. Set monitoring of MIDI input to In - this is in the I/O section of the track, there is a row of buttons In - Auto - Off. Enable Ableton's built-in MIDI keyboard (keyboard icon top right). You should be able to press keys on the keyboard - ASDFGHJKL - and see the MIDI level indicator flash in the track. Switch to Resolume, put it in MIDI learn mode (Res 3, mapping ; Res 2.41, preferences). Click (or double-click in Res 2.41) the parameter you want to assign, switch to Ableton and press the appropriate key. Ableton will send the MIDI signal over the loopback device to Resolume.
Note: this may not work 100% when running Resolume and Ableton on the same machine, since Resolume sometimes drops out of learn mode when it is no longer the foreground app. However, it works perfectly on two machines using IPMidi. (Note to developers: allow way of directly inputting MIDI note assignments to decks.)
IV. Test the connection
If you are using a MIDI controller, disable it for input in Resolume, and leave it enabled for input in Ableton.
If not, just use the computer keyboard in Ableton.
Leave monitoring to In in Ableton.
You should be able to trigger clips in Resolume by typing in Ableton.
V. Record some clips
In Ableton's session view (the grid), turn on record quantizing, to quarter notes. Double-click on a grid cell to make an empty 4 beat clip. Set monitor for the track to auto, and arm the track for recording. Start the new clip playing. Press some keys. You should see them recorded into the clip, and Resolume will simultaneously play them.
Keep adding clips. If for whatever reason clips don't play, set monitor to Auto for that track.
If you want some audio feedback, just make another MIDI track, put an instrument in it, and set it to take input from one of your clip control tracks.
That's basically it. From that point on, just play around and see what happens. It's interesting to use Ableton MIDI effects to modify the MIDI being sent to Resolume, try the arpeggiators and scales for example.
When you're comfortable with all this, you can enable MIDI clocking from Ableton to synchronize BPM, then you can clips speed up and slow down as you change the tempo in Ableton.