Summarize this article:

After the pipe has cooled, shake the pipe. Make sure to put a finger over the bowl so the ash doesn't go everywhere. Do this for a few seconds. Then, pour the ash and debris out of the bowl.  If you can't get everything out when you pour, use the pipe tool with the spoon end to scoop out the ashes. Shaking the pipe with the ash still in it helps to form cake on the inside of the bowl, which helps prolong the life of the pipe. After dumping the ash and dottle, blow through the stem to get rid of any excess ash and dottle. Then, use a pipe cleaner to clean the pipe. Start with a bristle pipe cleaner. Push the pipe cleaner through the stem of the pipe. The tip of the pipe cleaner should be the only part visible. Then remove it.  Afterwards, you can use the other side of the pipe cleaner or use a clean pipe cleaner to do the same thing. Do this until the pipe cleaner is clean when you remove it. Use a damp pipe cleaner to clean the mouthpiece. You can dampen the pipe cleaner with saliva. Rub the pipe cleaner around the mouthpiece to remove any debris lingering on it. Blow through the stem to blow out any ash or debris. Take a soft cloth to wipe down your pipe after you have cleaned the inside. To preserve the wood, you may want to use a cloth dampened with olive oil or a special wood pipe cleaning cloth.  Place the pipe on the shelf. If you are concerned about moisture in the stem, you can leave a pipe cleaner in it to soak up moisture.

Summary:
Shake your pipe. Clean the pipe with a pipe cleaner. Wipe the mouthpiece. Wipe the pipe before putting it up.