It's not a feature officially available on anything but the last few 
generations of mobile Macs, though (starting with a model of the 
PowerBook G4 IIRC). Even though, Apple - to the best of my knowledge - 
does not officially support hibernation on desktop machines (as the 
Mac Mini or Mac Pro), it's said to work for some after setting it up 
through pmset on a shell.

To put your Mac to sleep via Remote Buddy, select the respective item 
from Remote Buddy's menu (one of the last in the main menu by default 
- and also to be found under "System"). Additionally, with default 
settings, when no supported application is running, you can also put 
your Mac to sleep with the Play button.

You can also "hardwire" it to a button via the "Global mapping" table, 
but that of course will make the button unavailable to anything but 
that action.

Best regards, 
Felix Schwarz