Campfires are not always the easiest things.
I can count on one hand how many kayak camping trips I have done in the past half-dozen years when it was nice and sunny the entire time. I live in a place that has been given the nickname ‘Wet Coast’ for a reason. Even on a mid-summer trip to the west side of Vancouver Island I was met with no less than three intense frontal systems carrying a few hundred thousand gallons of rain. I remember the sun in between with fond memories. Keeping warm and doing some cooking on a campfire was key to not only the survival part of the camping trip, but also the moral.
I bring with me a small supply of dry wood (if I can fit it into the kayak) knowing that what I find out there will be damp and hard to ignite. That is the first step, the second is being able to light that dry kindling and keep it going long enough to start a good bed of hot coals that will be the base of your campfire. Once you have that base, drying out wet found wood will be an ongoing, but easy task. Stacking it close to the fire, but not too close as I found out one afternoon. Leaving ample airflow around the wet wood and adding it to your fire as needed.
To get your fire started there are a few things you can try. One of my tried and true methods is using a small tea light candle. Placing it on the ground and stacking small bits of kindling around it in either a square house style or teepee style. Keep adding small bits until the fire is glowing. The advantage of the candle is that it can be relit if something goes wrong and if it tips over the waxy wood will burn well.
Another fire starter idea is to stuff used toilet paper tubes with lint saved from your dryer. It is a good fire starter but will not burn continuously. A third option is to make your own firestarters at home and bring them along. A waxed paper cup cut in half and filled with a mixture of candle wax and wood chips and lint will work. Even steel wool will act as a grand firestarter.
Experiment, and find out what works best for the way you do things out there, but always remember to be careful and responsible with your fire. Make sure you build a good fire pit and on a level area being mindful of overhanging branches and anything flammable nearby.