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, where there is a Mages Guild Hall. Each city has a guild hall with a guild leader (Guildmaster) you can talk to. Examples include Carahil in Anvil, Kud-Ei in Bravil, Jeanne Frasoric in Bruma, Falcar in Cheydinhal, Teekeeus in Chorrol, Dagail in Leyawiin, and Adrienne Berene in Skingrad

• Speak to the head of the Mages Guild in any of these cities and ask to join. As long as you have no bounty on your head, they will grant you membership immediately and give you a Mages Guild Charter and a key to guild halls

• After joining, you need to earn a recommendation from each of the seven guild leaders by completing a minor quest or task they assign. These recommendations are necessary to gain access to the Arcane University in the Imperial City, which is the main headquarters and offers advanced magical services such as spellmaking and enchanting

• Once you have all seven recommendations, go to the Arcane University and speak with Raminus Polus. He will officially induct you as an Apprentice in the Mages Guild and give you the Robe of Apprentice, granting you access to the university and its facilities

• Be careful not to steal from or kill guild members; doing so will get you expelled, and you will need to gather special ingredients to regain membership

In summary, joining the Mages Guild is straightforward: ask to join at any guild hall, then complete recommendation quests from each guild leader, and finally get inducted at the Arcane University to become a full member