There are a lot of ways to start a fire and as many correct and incorrect methods to do so. There's nothing worse in a survival situation than trying for an hour to get your fire going and wasting all of your materials. I will post some tips for proper fire starting and welcome everyone to correct me if needed and to add their own tips.
Of course, the most important step of the entire process is good tinder. You need something extremely dry and combustible; good sources are cotton fluff, hay, straw and other dry grasses, leaves, and moss. Be ready to toss some dry twigs onto the tinder as soon as it gets going good. Then add progressively larger twigs and sticks until you can add branches and logs if needed. If the wood is wet then you will need to build a proper "tee-pee" fire so that the burning tinder and twigs are in the inner center and the larger sticks form the shape of a "tee-pee" on the outside, this will help dry out the outer sticks.
Waterproof matches are always a good option but I recommend Firesteel for sparking the fire. Firesteel uses magnesium shavings to produce a shower of sparks at approximately 5,000° F, they promise an easy job even with wet tinder.