Agreed with all the excellent advice already given. It's also good to ease into it. Start with easy stuff, and work your way up. Only do the work if it's scheduled or it actually needs fixing. The repair manuals from the manufacturer are excellent, and the cheaper manuals (Haynes/Chilton) are viable for the most part.
Super easy, no tools required:
--filling windshield washer fluid
--change wiper blades
--change air filter (might need a screwdriver)
--check oil, brake, and transmission fluid levels and condition
--check (and if necessary, fix) tire pressure (ok, this one requires a tool)
Still pretty simple, a few tools are needed:
--change a tire
--change the oil
--change transmission fluid
--flush coolant
Easy, but a good next step:
--Brake pads
Once you've gone as far as replacing brake pads, you'll have most of the tools and skills to tackle most normal maintenance and repair.