In The Elder Scrolls IV: Oblivion (including Oblivion Remastered), you can repair your armor in two main ways:

Repairing Armor in Oblivion

• Using Blacksmiths and Vendors:
  You can take your damaged armor to blacksmiths or armor vendors located in towns and cities across Cyrodiil, such as shops in the Imperial City (e.g., "Slash and Smash" or "Best Defense") where NPCs will repair your gear for a fee

• Using Repair Hammers Yourself:
  Repair Hammers are items that allow you to repair your armor and weapons manually. You can buy them from blacksmiths, general stores, and armor shops for about 10 gold each, or find them in chests and barrels while exploring, especially in the Market District of the Imperial City

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To repair, select the Repair Hammer from your inventory's Miscellaneous tab, then choose the armor or weapon to fix. Repair Hammers have limited durability and can break after use, but using them also increases your Armorer skill, which makes future repairs more efficient and reduces breakage

Additional Notes

• To repair enchanted armor yourself, you need to have an Armorer skill level of 50 or higher

• Leveling up your Armorer skill to 100 will allow you to repair any gear without breaking Repair Hammers

• Repairing via NPCs is convenient if you lack Repair Hammers or have a low Armorer skill, but it costs gold

In summary, you can repair armor by visiting blacksmiths and armor vendors in cities like the Imperial City or by using Repair Hammers found or bought throughout Cyrodiil. Building your Armorer skill lets you repair gear yourself more effectively and cheaply.