Camping is a Miscellaneous Skill used to secure your campsite to allow instant log-out. It requires kindling and a bedroll.
Kindling can be gathered by double clicking on your dagger, then targeting a tree.
Double click on a pile of kindling (kindling can be bought in towns or gathered in wooded areas) to make a fire. Your skill will be checked automatically, and if successful you will receive a message that your camp is secure. To log out from a camp, use your Bedroll in the vicinity of the campfire.
When you get the message about your camp being secure, drop your Bedroll, double click it to open it, and then double click it again. You should get a gump confirming you're about to instant log out. Click Okay. You will get a "Connection Lost" type of error, and your character is now completely logged out.