I'll be concise but don't think I'm saying this is the only way to do it....
If its a new pipe, don't really clean inside the bowl. Just remove unsmoked pieces of tobacco, but don't scrape the sides of the bowl with a pipe cleaner. If the pipe is well broken in and has a cake, in addition to removing unsmoked tobacco you can bend the end of a pipe cleaner to make a "U" and use that to swab the inside of the bowl lightly to remove ash.
After each smoke, I keep the pipe together and run a pipe cleaner down the stem, from the bit, to the shank. When its at the shank, and I can see it from the top of the bowl, I run it, about 1 inch, back and forth a few times, and then pull out the pipe cleaner and discard it.
I don't remove the stem very often so that it won't wear down (become loose) too quickly.
Once every two months or so, I'll do the above stem/shank cleaning after first dipping the tip of a pipe cleaner in some ever clear.
Once every 6 months or so, I'll take the pipe apart, and with a pipe cleaner dipped in ever clear I'll clean the shank until the pipe cleaner stays clean (doesn't pick up any more gunk).