Ableton has always offered a decent Live trial version, but now the company is giving you the opportunity to demo all of the software's features for a whole two weeks.
Previous trial versions haven't let you save or export your music, but the new demo gives you 14 days of full functionality. You simply have to download the Live 7 trial, register for a serial code and then unlock it with the number that you'll receive via email.
The only stipulation is that you have to be connected to the Ableton server in order to activate the save and export options.
Other than that, you're good to go – free to play with all of Live's features and instruments for two weeks. That should give you plenty of time to learn the software, and possibly even to finish a track or two.