Threads like this give me pause after a certain member (who is no longer active) gave a thoughtful response on a thread involving cleaning pipe cleaners. I do wish he were still here since the gentleman changed my perspective on responding to certain posts.
While I often try to sprinkle humor in some responses (which usually go over like a lead balloon), the OP in this thread is not trying to make arts and crafts; rather he is trying to figure out the proper way (if there is such a thing) on how to use a unique cleaner as a tool to clean a pipe for a more enjoyable smoke.
This is a pipe forum and people here generally smoke. Others come for advice and information. Without providing the same, the forum would be substantially different (and probably less enjoyable for myself and others).
To answer the OP's question: if one side is more coarse than the other, use the coarse side first if going through the stem to help break down the gunk (then the smooth side). If there is no gunk in the stem, use the fine side in the stem first, then fold the pipe cleaner in a U shape and use the coarse side to clean the chamber. The fine side can also be used to absorb moisture in the stem or dipped in alcohol and then used in the stem to help break down gunk.