If you go to any store catering to campers you'll see a large selection of firestarters designed to help you get your campfire going. Many of these work well, e.g., Lightning Nuggets, but it's simple to make your own firestarters for much less money. I made some today from cardboard, jute twine, and paraffin wax from the canning section at the supermarket.
To get the cardboard I cut the flaps from an empty beer case, then cut each flap into sections about six inches long. I then rolled up each piece and secured it with several wraps of jute twine, tied off with a square knot. Then I soaked each bundle for a few minutes in paraffin canning wax in an old pot on my charcoal grill. After a few minutes I took each firestarter out with a pair of pliers and set it in the bottom of the beer case to harden.
I tested one firestarter by lighting it with a match. It burned for several minutes with a good, high flame. It would work well to help get your campfire going if you had to contend with wet wood. Note that these won't light directly from a spark but are pretty easily lit with a match or lighter.
Be very careful when melting paraffin. The safest way to do so is in a double boiler. It's also a good idea to do this outside in case you have too much heat and the wax ignites.
Aside from rolls of cardboard you can use other household items to make firestarters. One of the best ways is to take the bottom of a cardboard egg carton and fill each pocket with sawdust or dryer lint. Use lint containing mostly cotton fibers, such as lint from drying a load of towels. Then, melt some wax and pour it into the egg carton. You then cut apart each pocket, leaving you with 12 to 18 firestarters that will burn for several minutes. Depending on how much help you need getting your fire started, you can even cut each of the firestarters into smaller sections.
Making your own camping gear is fun and can save you some money. Give it a try.