I was a SERE (Survival, Evasion, Resistance, Escape) instructor in the USAF and station at Fairchild in Spokane. We did our tropical/rain forest training in the Ho national forest.
Cotton balls and Vaseline are my favorite fire starter. They are light weight, take up no room, are readily available, and multi use. One or 2 cotton balls soaked in Vaseline, and then aerated very well is all you need. It will easily catch fire with a spark. I recommend a metal match for this as matches get wet and lighters can break or run out of fuel. I have started thousands of fire with the same metal match (magnesium stick, etc)
Build some type of platform to get the tinder and wood off the wet ground.
On the platform, place a brace that is about the size of your forearm. This is used to keep the 1st stages of wood off the tinder so that you can get oxygen.
Fire needs 3 things, heat (metal match) oxygen (brace) and fuel (cotton balls and your firewood)
As far as wood goes, pitch is my favorite, and I would always have a chunk on me when I was teaching. You can also use the pitch wood (fatwood) as a tinder by scraping it with your knife and creatinging wood shavings. Best place to find pitch is in stumps. If you see a big shard of wood sticking out of a rotten stump, its probably pitch.
Next easiest is what we called squaw wood. It is the lower branches of pine trees. Preferably with good cover above to protect from the rain. Get a big armload of this, break it into pencil lead, pencil, and thumb sized pieces and put that on the tinder in the smallest diameters and work your way up. I prefer a grid or log cabin style to start and then can use the teepee overtop of that if you have some bigger chunks of wood that might be a little wet.
If everything is soaked, then you have to get to the heart wood. Dead standing with bark still on it is the best if you can cut it or break it. Wedging between 2 trees and breaking will work in a pinch if you don't have an axe. Mini chainsaw in a can work good too. Its just the chain with 2 handles on it. Can saw half way through a coffee can sized tree and start rocking it and a lot of the time you can get it to split for you.
Thats about it. If you are going to be out in the backcountry and there is a chance that you could need a fire to save your life, then I strongly recommend practicing both a squaw and a split wood fire and be prepared just in case you ever need it.