Numbers that mark each stamp in the pic correspond to the numbered directions below.
#1-3: Click on the prom couple (Uptown/Downtown) and play the 3 games (Click here for the guide)
#4: Go to Uptown/Downtown and vote (you can do this every 10 minutes and get 10 starz each time)
#5: Click on the Limited Items Cart (Uptown/Downtown)
#6: Click on the prom couple (Uptown/Downtown) and watch the movie
#7: Get your free gift (Downtown). New one every day, check this post daily to see what it is.
The medal for completing the stampbook: