I've heard of people who dig up their existing plants and set them off to the side in pots while they add compost and till the entire garden. That kind of overhaul is extreme and only necessary if, one, you love labor, or two, your garden is in such atrocious shape that a complete overhaul is necessary. The simpler method, which is perfectly appropriate for 99 percent of established but "tired" gardens, is to add a thick layer of compost on top.
If you don't have your own compost, try to find some that is lightweight and crumbly; avoid the heavy, mucky stuff. Spread a 3-inch layer everywhere you can. If you're worried that self-seeding plants won't come up through a layer that thick, you can skimp in some places, but plan to add another layer of compost in the fall and again next year. Beneficial soil organisms actually feed on the partially-decomposed plant material in the compost. Their activity will slowly but surely improve the soil below.