I heard that the patriciers organised games in their honor but did this mean that they payed for it all. Or was there a ticket fee or something? I know the question is a bit vague but I just don't get how the whole idea of the gigantic Colosseum worked.
There were no ticket fees. Regarding who paid, Rome had at least two types of "public" events.
Munera were events paid for by wealthy individuals in order to show their generosity and curry favor with the people. These would include gladiatorial games.
Ludi were games (like chariot races, etc) that were paid for by the state. They were held on holidays and had a religious/ceremonial aspect to them.