How do you get a follower in Oblivion?

Answer 1

At the end of the dark brotherhood questline when you are the listener, the sanctuary will be repopulated by up to three generic assassins. You can get one, and only one, to follow you. They can follow, wait, follow invisible and follow you as fast as you are going. At the end of the mages guild questline you can order one mage student to follow you from the arcane university. They don't have as an elaborate order system as the assassins, with only follow, wait or go away. When you are the grand champion in the arena there will be someone called "Adoring Fan" outside who basically worships you. If any of these people die, they will continuously respawn at their respective locations.

Answer 2

Unfortunately, there are no true 'followers' in Oblivion. I'm guessing you have played Skyrim, if you are asking this. The closest thing you can get to a follower is completing all the Arena challenges in the Imperial City and becoming the Grand Champion (by defeating the current one). You will then meet a NPC called the 'Adoring Fan', who is a really stalkish elf. He is of absolutely no aid in combat, but will follow you around. He does, however, carry a torch which can be useful if you don't want to carry one yourself.