Rainy conditions makes lighting a fire really hard, and sometimes, to tell you the truth, impossible.
I know a lot of people feel like camping without a fire isn't camping, and I'm kind of one of those people. But if it is raining really hard while you are camping, you're going to have a really hard time lighting a fire. The other thing you could run into is that if you’re camping in a place where it has been raining heavily for a long time, a lot of your wood could be really saturated, and very wet, and you may also have a very hard time lighting a fire.
A couple of tips that you can try. First, if you use a fire starter, because if it's raining, you are going to have a hard time actually even getting a flame at all. If you use a fire starter, something like cotton balls dipped in petroleum jelly, that's a really great fire starter and it will just burn and burn and burn. So what you can do is take the small stuff, which is the tinder, which is these little, little twigs, leaves, and some paper would be great if you have paper left over from camp.
That stuff wrapped with a fire starter could possibly get you some flames that will go for maybe five or ten minutes. So if you can get that going, you can start to put on the larger stuff, which is the kindling, like this, and even though it might be wet, it will start to dry out. If you can get the flame going at all, and you get it to last for a little while, you can hopefully get some of the kindling to dry. Then, you can start to put your other wood all around the fire that you get going, and hopefully it will start to dry out more. It will steam, it will smoke, that's just the water coming out of the wood, and that's really the only way to do it.
So a fire starter is a great thing to have if you are going to a place that might be raining. In fact, a fire starter is just great to have, period. Because you never know, and you can just hope that you can get something going enough that you can dry out the wood that is available and hopefully get the fire going, and get it big enough that you can get a log to ignite. Once you get a log to go, you're good. It would have to take a lot of rain to then put out the fire.
So, if you can get enough flame to get the logs going, you will probably have a great campfire that night. It's just getting there that is the challenge. Lighting a fire in wet conditions is a lot of work. It takes a lot of patience, and a lot of fiddling. You kind of have to be prepared for that, or just say “noo fire tonight” and roll with the punches. That's kind of what camping is all about anyway.