'Tune-ups' are not like they once were. Today's cars have lots of computers and sensors that check on everything as the car goes and adjust what is needed. Tune-ups used to be to adjust things like carbs. That said, your car still needs regular maintenance.
Check your owners manual. In it will be a complete list of things that need to be done at each service interval (10,000 miles or whatever it is). Generally speaking it will be replace the oil and filter, grease door hinges, top up windshield wiper fluid, and do little else. At larger intervals it will involve more complicated stuff (check/replace brakes, change transmission oil, replace spark plugs, replace timing belt, etc).
For the small jobs, you can do it yourself without too much difficulty (if changing oil was hard, walmart wouldn't be paying high school students minimum wage to do it). For the larger jobs, I'd take it to a garage or dealership. If you've got a local garage you trust, I'd go there first as dealerships will charge a lot more. That said, I have a good relationship with my dealership and take my car to them.