I hope this helps the OP question.
Step 1.) I clean the stylus with the stylus cleaning brush that came with my Lyra cartridge. I also have a Discwasher Stylus Cleaning Brush since 1975 but it's fairly large and the Lyra is nice and small. They both provide the same results though, so as long as you get a brush that is specific for stylus cleaning you can't go wrong. Follow the directions that come with the brush. These are stiff bristle brushes and are very different from a brush for use with a cleaning agent. That said, I use the brush after every 2 sides of record play.
Step 2.) After every 6 to 8 sides played I use the Lyra SPT Stylus Cleaner. A bottle comes with a very soft cleaning brush and that is what I use. Though it is expensive ($60), it will last about 5 to 8 years, depending on how many records you play per week. I play about 12 to 15 records per week and my bottle of Lyra SPT is about 25% used in about 1 3/4 years of use.
Following such a cleaning regimen is like keeping your tires balanced and rotated. You will get the most life from them by doing so. As well, you will get the most life out of your stylus by keeping it clean. Record care/cleaning is another topic, but you asked about stylus cleaning so I remained specific to that. I hope this helps you.