Yes,important to clean the stylus. There are brushes & other devices made just for that. Until you get one, use any small brush to brush the stylus a few times, from back to front only, before each record you play. 

How does one clean the stylus cleaner?

The cleaner usually has an applicator much like fingernail polish that you dip in the solution and gently "paint" the stylus from back to front, careful not to push or bang into the actual stylus. There is also usually a small brush that you use in the same manner to remove lint and dust.

I clean mine after every record.

I use LP-9, but Last is probably the most popular.

I try to clean the stylus between each needle drop, but I ALWAYS clean the stylus before & AFTER each session.

Most cleaners come with a small brush.
Be cautious; always brush in the same direction as the record moves over the stylus.
Some others are like a mushy gel on to which you drop the needle.
Again, just be cautious......never be in a hurry..... especially when imbibing listening enhancements of the distilled character.

Anyone who thinks this is a joke has never spun vinyl for long.
I freely admit to once trashing a wonderful fine-line stylus due solely to getting in hurry for no good reason while in the presence of an otherwise quite well behaved Côtes du Rhône.

I also realize this may be asking far too much, but try to read the instructions that come with your cleaner.

Bill - on the Hill
Practicing Curmudgeon & Audio Snob
- just an “ON” switch, Please –