Clay feels a little like harder "Play Doh".
It will remove contamination from the paint finish (and also glass) that cannot be removed using conventional cleaning methods. I've used it to remove paint overspray, bugs, tar, tree sap, water spots, & rail dust. Most auto parts stores carry it but you can also buy it at some of the major/premium car care vendors on the Internet. I use diluted car wash and glide the flattened claybar over the surface. It should glide and not bind against the surface of the paint.
You should first ask you painter how long you should wait after painting in case there is some sort of warranty on his work. You should follow those recommendations. New Corvettes are ready to wax/polish when you pick-up the car at the dealership. The following is taken from a quote from Sal Zaino that I saved from 2001:
For the most part there's alot of misinformation about waiting three months for the paint to cure. I am a custom painter by trade. I am very familar with Dupont, PPG and all the other paint manufacturers. The most I personally would wait on fresh "aftermarket body shop" paint before polishing with Zaino Show Car Polish is 1 week. That's more than sufficient curing time. The new paints are catalyzed. A chemical reaction cures the paint. The older lacquers and enamels needed time for the solvents to release. This is not the case anymore. Believe me if that paint need 3 months to dry than it will never dry. Just the facts.
The wax/polish business is very competitive. Guru Reports published "the Wax Test" in 2002 testing 46 different products. Hopefully saving you a few dollars in the process. I believe they are working on another version of the test. You should still try a few because not all products suit the needs and personal preferences for everyone.