You need good dry tinder, dry kindling, and dry fuel. The key here is "dry". Normally, you'd at least bring starter tinder with you. Then you can add that to a locally sourced tinder bundle. Then start adding the kindling. Since it is wet there, like it is wet here all the time, you should look around for dead standing grass. The tops are usually the driest thing you can make a tinder bundle with that gets directly rained on. It helps to get stuff that is exposed to direct sun and not hidden back under something. Feather sticks are your best friend. Make them from sticks that are about two fingers thick. That makes it easier to do. You can feather up larger stuff and smaller stuff if required, but larger stuff can also just be split since the inside will be drier.
Papery tree bark usually has a layer you can fluff up to make tinder. I suggest making a nice big tinder bundle, even if you have stuff like lighter fluid. It make take 30-45 minutes to source everything and build the fire before you actually light it. You want to get it right the first time. If you have a magnesium fire starter, those are great for wet weather fire starting materials.
Basically, for everything wet, feather it and/or split it open.