The Rust Monster (MM p.262) can inflict a "permanent and cumulative -1 penalty" to the damage of weapons, or to the AC of armor or shields.
Is there any way to repair this damage?
So, firstly if you want a specific written rule on how to repair rust-monster-damaged weapons and armor, you're not going to find them in the currently published rulebooks.
The key word here is 'permanent' which can have two interpretations, again not specified by the RAW.
If you take 'permanent' to mean 1, someone with Smith's tools proficiency and access to a forge (and some extra metal) could repair the armor and shields. After all, the weapons are not destroyed until they are at -5, and armor until it reaches AC 10, so there must be some salvageable metal under the rust.
If you take it to mean 2, all is still not lost. Lesser magics like the Mending cantrip won't cut it, as they are only meant for repairing breaks and tears, but if the Wish spell can repair Daern's Instant Fortress (DMG 161), then a few rusty swords shouldn't be a problem.
But as the Rust Monster only damages nonmagical weapons and armor it seems like in most cases it would be less trouble to buy some new gear...
Well we could take this into the real world to answer.
A fine layer of rust will have no appreciable affect on a sword or armor's effectiveness, though it could make joints stiff.
However, if the amount of rust is enough to appreciably reduce the effectiveness of the item, then it means an appreciable amount of material has been lost.
You can't just add another layer of forged or smithed material to a sword or shield to restore it. You would effectively have to recycle the item for its material and smith a new item from the reclaimed metal.