Well, it depends a little on context, but games are played in a stadium. I could hang signs on a stadium.

"On a stadium" means "on top of a stadium". This might mean a flag, but nothing much else. Randy's example of "in a stadium" is probably what you need. If you write "a game played on a stadium" that means the stadium probably has a huge roof and the players are not on the field, but up on the roof instead. If you go to the stadium to watch a game in the stadium, then you are (as a result) "at the stadium".

Usually, we use "on" for flat things: (on T.V., on the grass, on Earth, on the table, on a ship, on a stool) We use "in" we mean "inside": (in a book, in the bathroom, in a rowboat, in China--countries are like rooms, in Los Angeles-cities, too, in his chair--a chair has sides, so you can sit in it.) We use "at" for places. Confusing, right? We can say "at the stadium" or "in the stadium." Both are correct. I'm at the stadium--I'm at that location If my friend calls me and says "Where are you?" I will say, "I'm at the stadium, watching Real Madrid." I'm in the stadium--I'm not outside, I'm inside If my friend calls me and says, "Hey, I'm in the parking lot. Where are you?" I will say "I'm in the stadium. Come inside." This is one of the hardest skills in English. I made a video about some common mistakes, if you want to take a look: http://www.youtube.com/watch?v=AjQJHkODzq4 Have a good one. -Dan

on a stadium