I second the Magic Eraser. I put crazy-glue on a plastic coffee stirrer and jamb it into a sugar-cubed size piece. Then with the TA in its rest (locked down) I lift it up against the stylus/cantilever and then back down. No back-and-forth action! Not necessary -- I've checked w/ a scope. THEN I use the ZeroDust to remove any particles. I've found it removes more than a soft brush, there's no risk of damage, and most important (again I've checked this w/ a scope) the ZerpDust removes the crap in that pesky spot BEHIND the stylus up near the cantilever -- whereas brushing (back to front) won't get rid of it.
Grain alcohol (Everclear 190 proof, almost 100% grain alcohol) dampened on either a vdH or AQ -type stylus brush or on one of the original vibrating versions (uses the same kind of brush) will get rid of the glaze Doug mentions, but only if you use the 100% grain alcohol. "Dampened" means you put several drops on the brush 'til it saturates, then just before use (100% grain evaporates in a flash) press the brush against a tissue or clean cloth and use immediately. There's no chance of any getting up the cantilever this way (it evaporates too fast anyway!) and it will get a stylus absolutely "sparkling" new.
I'm totally against any kind of stylus conditioners (StyLast, etc.) First of all, I can't imagine any kind of coating (except maybe epoxy!) sticking to a stylus through more than one rotation of a record! And there exists a real possibility of it travelling up the cantilever -- and besides, how are you supposed to get the build-up off the cantilever after several applications?!
If you want to improve the stylus/vinyl interface, treat the vinyl. I really like Last preservative. I know a lot of people don't, and I don't use it on every record myself, but here's what it does: Vinyl has a lot of volatile compounds in it (stuff that evaporates out in time like "new car smell") An older record (over 10 years, not sealed) will, to a greater or lesser degree, lose enough of these compounds to cause a certain amount of microscopic crazing (like a dry riverbed or old furniture finishes). Last replaces these compounds. It can't repair the microscopic cracks of course, but it causes the vinyl to "swell" just enough to close them up.
The "problem" with Last Preservative, is that no amount of post-treatment buffing will make the record immediately playable, nor will a quick spin on your vacuum record cleaning machine totally get rid of any excess. You simply have to play the record at least once so the stylus pressure can "squeeze" any excess out of the reconditioned vinyl. Other than that hassle, this is not bad thing for the stylus, which I've checked afterward, and the residue seems to come away cleanly with just a ZeroDust.
The good news is you only have to do it once every 10 years ;<)) It will not be affected by subsequent cleanings with record solutions, if they don't have alcohol in them.
