How do you close an oblivion gate on oblivion

Enter the gate
get to the top of normally the largest tower or whichever looks most important
Enter the sigil keep (room at the top of the tower) and take the sigil stone (firey ball)

If you don't want to complete all these oblivion gates (since there are a lot of them and rather challenging) completing the main story line will close every single gate on the game. However, you wont get the sigil stone which is useful for weapon and armour enchanting.

"-Father Dagon-"