I would try to find shelter first wether it be a tree or natural formation. If you have someone else with you, split up the jobs of making a wind break/shelter and finding kindling/fuel wood. Get lots of kindling/fuel of various sizes, more than you are used to.
If you have a large knife or axe try to split smaller logs to get to the dry core. By splitting it into wedges not only do you get the drier interior but you also get more surface area.
As for tinder and kindling, it will depend on where you are. Try looking at the bse of a large tree and dig well below the ground cover. Be creative. I have burned the normal firestarting stuff but also rubber from a ranger band and some other nasty stuff to get the fire going. Do not breathe this stuff, it be real bad for you! I have used pitch wood that was given to me by a friend. I live in Hawaii so it is hard to find. We have some stuff here that burns well.
When you get the fire going, I try to keep it small and start drying out the smaller wet wood first. We have also made multiple fires in a driving rainstorm because we were worried that if we had one fire it may be extinguished by the rain. Another technique is to dig at the base of a tree for dry dirt and place it on a platform of logs made into a "tabletop". This keeps the tinder/kindling drier during start up.
I like to only have one or two people working on getting the fire going when there is a group, it keeps the chaos to a minimum.
Go and practice a lot. Fire building is a skill that has to be maintained. I haven't done it in awhile, it would take me a few tries to get it going now. I would try it in your backyard when it is dry a couple of times first then give it a shot during the next rain with a lighter. After you master that try using matches. Then try it with primitive methods. Try with half of a paper match from a matchbook. I have heard of POWs in WWII splitting wooden kitchen matches with a razor into multiple pieces and starting a new fire with each piece. To me that is an amazing skill.
Practice and good luck!