My younger DD17 was Geo Bee state finalist (CA) for 3 year in a row. Her best result was 7th place at state final and the only girl in the final 10.
Like any worthwhile endeavor, Geo Bee requires a lot of hard works. Hours and hours of map studying, flash cards querying of geography terms, counties, capitals, etc. There is no after-class program that I know of. It is more a lonely pursuit, usually involving mom and the kid.
Winning school round should be fair easy. Assuming the kid had done his home work. Then there is a written round for all school winners that select top 100 to state final. That is fairly easy too. At the state final, the purpose of the elimination round is to send to top 10 to the final round. So the student can't make any mistake or they will be eliminated. This is very tough. If he survives with no error, he will be on the stage with 10 other students (sometimes more than 10). That is more or less like Geo Bee national final that you saw on TV. One winner from a state is sent to national final. The California Geo Bee, during the years my DD was competing, was dominated by a boy in LA area. He was the state winner 2 of 3 years. But he did not do that well at National.
This following book is the must have for Geo Bees:
http://www.amazon.com/Afghanistan-Zimbabwe-Country-National-Geographic/dp/0792279816