There are, at least, two ways:
1) By BIOS with automatic power on function. Check if yours have such kinf of funcionallity. Usually the configuration resides under Power Control. This is the most simple and I guess is what you are looking for.
2) By NIC with WOL - Wake-up On Lan - support - again; check if your NIC has WoL support. In this case, another computer will send wol commands to your machine. So you need to setup the command to run at specified time in that computer, using "cron" or "at". There are several WoL projects on linux, google is your friend. Just to mention 2:
http://freshmeat.net/projects/wol/ and
https://sourceforge.net/projects/wake-on-lan.
cheers,