How do I turn a rocky area full of weeds into a decent garden area?

First thing you need to do is get rid of the dirt with the rocks and the pebbles; don't try to clean it up - sounds like that would be a waste of time. If you can dump it in a hole, that would work perfectly. Then, cover the area with topsoil, but the top layer should be GOOD QUALITY potting soil or worm castings a.k.a. vermicast. Both of these soils are loaded with nutrients and time-release water and nutrients to your plants to make sure they get what they need when they need it without drying up or drowning. Worm castings are better than potting soil, but DO NOT use worm castings if you're planting vegetables. This stuff may attract worms that could eat your veggies. Good luck!