After I beat the gym I was confronted by May with the Go-Goggles after that I went to the desert but I don't know what to do there. Do any of you guys know?
Desert plus Mirage Tower for the Root Fossil or the Claw Fossil (requires Mach Bike and Rock Smash) or head straight to Petalburg and battle everybody in the Gym.
Also you can get a Fire Stone and the Toxic TM in Fiery Path by using Strength on the way back to Petalburg if you take the north route.
The desert is completely optional but you can battle the trainers there, catch the desert exclusive Pokemon, get one of the fossils from the mirage tower if you want and get the sandstorm tm.
What you have to do now to progress is go back to Petalburg city to battle the fifth gym leader Norman (your character's dad). You get the surf hm after beating him so then you can continue to the east of Mauville.