There are two kind of envelopes in Live, clip envelopes and automation envelopes. These can be added via MIDI controllers or drawing. Or a combination of both.

To draw envelopes, you need to turn on the Draw Mode by either clicking on the pen icon in the Control Bar or by pressing Ctrl + B (Win) or Cmd + B (Mac) (up to Live 8), or B (Live 9 and up). Now you can simply draw the envelope curves. Steps are created according to the grid settings.

You can use the commands I described in part 1 of the Workflow Tips series to widen or narrow the grid. For freehand drawing you can turn off the grid with Ctrl + 4 (Win) or Cmd + 4 (Mac). If you want to still see the grid, but enable freehand drawing, simply hold down Alt while drawing.

I personally love using this feature to automate track panning. What do you (want to) use it for?

Missed the other tutorials in the series? It begins with Ableton Live Workflow Tips Part 1 - The Editing Grid.