There are several ways to ban a player. The easiest is when they send you an insult via an ingame message.
If this happens, you will notice a checkbox that says “Ban this player”. Simple check that box, and process your messages. This will automatically ban the player for 24 hours. NOTE: You can ban fellow alliance members this way, so please be careful. Sometimes a word will trigger the filter, even thought it isn’t insulting.
For any other bans, please contact an OGame Game Operator (called a GO). Have proof of what happened (bashing, insults, pushing, etc) and the GO will investigate.
You can see the OGame Pillory (List of banned players) by Universe here. It is a good place to see how long someone is banned for, and why they were banned.