How often, and how, do you clean your stylus?

That's a very personal and inappropriate question. For shame!

I clean only when it sounds like it needs it. Couple of times a year with many hours of playing in between. With this hobby, I don't look, or listen, for problems that aren't there. 

I do similar as @snilf only with the Japanese Onzow device on a little purpose-built riser. Volume on, to listen for contact.

Seconding @mijostyn ‘s concern for blue tack. There’s also a greasy component to that stuff (why you should also never use blue tack on paper / posters you plan to re-use or keep in clean shape) and I’m not sure whether that would affect the stylus (whether for better or worse).

I cut a round piece of Magic Eraser (lots of praise for this product used for this purpose) to fit into the cavity of a trimmed rubber furniture foot, which then sits on my turntable plinth between platter and tone arm rest. I lower the stylus onto the Magic Eraser as I'm cleaning the vinyl with an Oracle brush. Do this every side. Stylus is always perfectly clean, and the procedure takes no effort whatsoever, nor does it risk harm to stylus or cantilever. 

The best and safest way to clean a stylus effectively.

Get a 1/8" wide artist brush and with a very sharp scissor cut the bristles halfway down and across at a right angle. This stiffens the bristles a bit. You can use it dry to knock of dust or wet to clean off residue. I use a little spray bottle of eyeglass cleaning solution. You do not want the brush too wet, just damp is fine. With an artist brush you can safely brush the stylus in any direction. 

Blue Tack is dangerous and ineffective. It will remove dust but not residue. One false move and you snap your cantilever off.

Lyra Stylus cleaner is awful especially when you consider the price. The eyeglass cleaner is way better and cheap to boot. It removes deposits quickly with just a few brush strokes. The Lyra frequently did not work at all. Alcohol will not effect the cement used to fix the stylus. Prolonged exposure to acetone would and perhap lacquer thinner. I once took an old broken cartridge  and tossed it in brake cleaning fluid overnight and the stylus was still well cemented in the morning. I have also done this with records with no noticeable ill effect.

I clean the stylus about once a week. I use a conductive sweep arm during play and the dust cover is always closed. I hardly ever have dust on the stylus, but a small amount of residue will collect above the contact patches. It does not affect play until it is severe enough to see with the naked eye.

@mojo771 

Wow. Assuming he is not playing albums 8 hours a day, there is something very wrong. I have never replaced a stylist and only had two cartridges in the last twenty years. I probably played one album a day when home… so about 200 hours a year? 

Before every listening session of 1-3 LP's.

I clean after 6 - 10 sides.  I rotate between Blue Tack, Disc Doctor cleaner / brush and a  cleaner / brush that was recommended by Lyra for their carts.  

I have a friend who uses his brush every single side. He has also had to replace his stylus 3 times in the last 3 years, so it seems like over brushing may do more harm than good.  He also Used to use the liquid, but the first time he had to have his stylus repaired the guy said it was covered in gunk.

I use a self-adhesive stylist cleaner (drop the needle on the gel once) each side or two. 

It’s as much or more of a bother to look at the stylus with a magnifier as it is to just routinely clean it without inspection. I do so with a Stylast brush (no fluid; just the dry brush) or with Magic Eraser or with a brush and fluid I bought in Tokyo. Once a year or so I inspect using an Olympus lab microscope.

I clean it before each side played and you are wrong, that is not excessive.  Every time I check any of my styli under my microscope there is almost always a bit of debris clinging to the stylus or the cantilever.  I also use a record brush before each play and run records through my RCM fairly often.