Cleaning a pipe is, for the most part, a fairly simple task, but it can also get rather involved if more intensive cleaning is required.
After finishing a bowl, simply remove the dottle from the chamber by using the spoon-like part of a pipe tools, being careful not to gouge the cake or the wood. Then, feed a pipe cleaner through the stem and shank. If a cleaner will pass all the way through to the bowl without disassembling the pipe, there is no reason to take it apart. If the cleaner gets tied up due to a severe bend, or just because of the design of the pipe, you will need to remove the stem from the shank. PLEASE, do not remove the stem while the pipe is still warm. If you do so repeatedly, it will stretch out the tenon and it will eventually become loose. In most cases, the above is all the cleaning routinely required. From time to time, more involved cleaning is desirable. As far as dull stems go, the simplest solution is to use a mild abrasive to remove any dull or grey spots. While there are some excellent commercial items available (like Denicare or Brebbia polishes), if the stem is not too badly stained, try hand-buffing with a bit of toothpaste.
If you want to polish up the briar, the best bet will be to use Briar Pipe Wipe, which comes in a spray can. All you need to do is spray a soft cloth with the polish and let it dry. Then just rub the wood with the cloth (the dried residue is all that’s needed to shine up the pipe). The shine will not be a high-gloss type. If you want a mirror shine, a low-speed buffer and carnauba wax are required, but this is something best left to a professional, as it takes very little to damage or burn a pipe with a buffer. Don’t use furniture polish to shine your pipes as the odor will become very noticeable when the pipe gets hot.
Reaming a pipe should be done when the cake becomes about the same as the thickness of a nickel. Using the correct type and size of reamer, slowly cut the carbon back until it’s about the thickness of a dime. Choosing a reamer will depend on how many pipes you will ream in a year. If you only need to do so once or twice a year, a decent pipe knife blade will do fine (but it does require a steady hand), but a simple self-adjusting reamer like the British Buttner would be best. For more frequent use, the interchangeable blade Pipnet reamer or the heavy-duty Senior reamer are preferable. In any case, if you are doing your own reaming, go slow and work gradually to avoid doing damage.