You can expose the dry inner of thin sticks (assuming, of course, that they're just damp on the outside and not wet through) by using your knife to make frizz sticks. The small shavings catch fire quite easily. If left connected to the stick, the flames dry the stick out enough to catch. Even a small knife (I have a Leatherman Micra which has a tiny blade) will do this easily if the blade is kept sharp.

If the wood is really wet, of course, you do need some kind of fire starter as suggested above. The fire starter will dry out the twigs or frizz stick shavings enough so they will catch. In turn, that will dry out the slightly larger sticks, etc.

I must admit, my fire building skills are somewhat rusty since I rarely build one. Never try to show off your "one match fire" skills to grandchildren after ten years of not making a campfire!

With an extra dry summer coming up out here on the west coast, I certainly won't get a chance to build any fires this summer! We've already had wildfires in January!