How to clean my soldering iron tip or how to determine that it's beyond repair?
(Solid) tip "tinners" are almost always ammonium phosphate with some tin (or tin-lead) bits mixed in. They are moderately aggressive at cleaning oxides off, so shouldn't be used constantly, but only when needed.  The best tip tinner is your solder--tips should always be coated with a small amount of solder.

If some of the oxides are just sticking really well, you could try to mildly abrade them on a brass sponge, copper braid, or similar, but you can't be too hard or you will damage the iron plating (good tips are typically copper core, plated with iron, then chromium everywhere but the working area).

Practice good tip care. I use a Hakko iron and tips at work and mine has lasted about a year (moderately light use, maybe 5-6 projects).  Put a good amount of solder on the tip when storing it or leaving it idle for any length of time; don't, for instance, wipe it off, put it in the holder, then leave it on over lunch.

Additional guides:


Hakko Tip Life Checklist (PDF, attachment to above KB article)
Adafruit Tip Tips (PDF)