To join the Mages Guild in The Elder Scrolls IV: Oblivion, follow these steps:

• Visit any major city in Cyrodiil except the Imperial City and Kvatch, and locate the Mages Guild hall there. Each city has a guild hall with a leader you can talk to

• Speak to the head of the Mages Guild in that city and simply ask to join. You must have no bounties on your head to be accepted. Once you ask, you will be admitted immediately and receive a Mages Guild Charter and a key to the guild halls

• After joining, you need to earn letters of recommendation from the heads of the Mages Guild halls in all seven major cities (Anvil, Bravil, Bruma, Cheydinhal, Chorrol, Leyawiin, and Skingrad). Each leader will give you a unique quest to complete before granting their recommendation. These quests vary in difficulty and can be done in any order

• Once you have all seven recommendations, travel to the Arcane University in the Imperial City and speak with Raminus Polus. He will officially induct you into the Mages Guild, promote you to Apprentice rank, and give you the Robe of Apprentice. This grants access to the Arcane University where you can conduct spellmaking and enchanting, which is exclusive to guild members

• Be careful not to steal from or kill members of the Mages Guild, as this can lead to expulsion. If you do, you must pay a fine in rare ingredients to regain membership

In summary, joining the Mages Guild is straightforward by asking any guild leader in a major city, but gaining full membership and access to the Arcane University requires completing recommendation quests from all guild halls across Cyrodiil