Tip from Bowshooter.com: Have you ever been out in damp or rainy weather and needed to start a fire, but had nothing dry enough to use? Here is an old trick that Scout Masters have taught for years. Buy a bag of 100% cotton balls and a large jar of Vaseline or other petroleum jelly. Saturate the cotton balls in the Vaseline. Some do this by hand, others melt the Vaseline down to liquid form and pour it on top of the cotton balls. If using hot Vaseline, place the cotton balls on some aluminum foil or an old baking sheet that you don't need anymore. Allow the soaked cotton balls to cool completely. Use extreme caution with hot petroleum jelly. It will leave a nasty burn on skin. Store the fire starters in a quart-size zip top bag, film canister, etc. This item will take up very little pack space and weighs next to nothing. When in need of a fire starter, simply take out a saturated cotton ball, place it where you want your fire (not in your hands), open it up to expose the cotton fiber, and start the fire with a match or lighter. Once the ball is burning to your satisfaction, add kindling. Before you know it, you're on your way to being warm and dry.
Just use your knife to shave some tinder off of a stick. Start with some really thin pieces. They will light, even if damp. One other thing, rained on dead wood that has seasoned will be wet mostly on the surface but you can shave that off with your knife to get to the dry parts.