As others have implied, this is no small request. All of the following are subjects unto themselves.

Learn how to adjust your derailleurs. The manufacturer of your groupset should have online instruction manuals.
Learn how to inspect and adjust your brakes.
If necessary, learn how to replace your brake/shifter cables.
Clean/inspect your drive train. The chain will probably be the first to need replacement. Learn how to check it, clean or replace if necessary.
Inspect the crank set; see if it spins freely with the chain off. If not, find out how to pull it apart, what to clean, how to inspect for wear, where to apply fresh grease and how to put it back together.
Check your tires for wear.
You may want to check with an LBS about servicing your hubs, if it's been a while. If you're ambitious and you don't mind grease, you can tackle this yourself, too.

You can take care of a good amount of the basics with a couple screwdrivers and a set of allen wrenches. If your bike has a lot of carbon bits, you'd be smart to get a torque wrench. Even if your bike doesn't have a lot of carbon bits, it's still a good idea.