"C'mon baby light my fire... try to set the night on fire!"
~ The Doors, Light My Fire
Homemade Tinder:
There are some great types of tinder that you can bring from home. For example, shredded paper, dryer lint, sawdust, and balled-up newspaper or notebook paper all work well. I like to mix in some dry twigs or bark with my homemade tinder so that I'm sure I have at least a little bit of dry wood to start my fire. Putting this in a small baggy can make your life much easier if it's snowy or rainy when you arrive at your campsite. If the ground is wet or snowy place something between your tinder and the ground before you ever lay it down (for example, a large piece of bark, a log, a piece of cardboard, etc.) so that your tinder doesn't soak up the moisture beneath it. Corn chips, tortilla chips, and potato chips all have enough fat (oil) in them to burn quite nicely while you collect some twigs.
The best kind of tinder you can make at home is known as "charred cloth" or "char cloth". It is created by putting some scraps of cotton into a small tin (Altoids mint tins work great) and placing it in the coals of a campfire. Once the campfire has burned around the tin all that will be left will be thin blackened strips of charcoal. This material is delicate, so be careful handling it. Your work will be well worth your effort it making it - a single spark can be held in scraps of charred cloth and with some light blowing it will smoke and then catch fire.
Natural Tinder:
If you weren't quite living up to the whole "Be Prepared" thing, or if you were packing light, you may be forced to find some natural tinder to start your fire.
Birch Bark
The bark of the birch tree peels off in thin layers and does not damage the tree if you select only the upper layers - it has large amounts of oil in the bark, and it is known for lighting even when damp. The bark of some varieties of the cedar tree works similarly.
Wild grapevine grows in most forests and burns wonderfully - make sure you are dealing with grapevine and not Poison Ivy or you could create a serious first aid situation. Live grapevines have small curly tendrils coming off of their vines near their leaves. As grapevines age the vines turn brown and appear as though they have thick bark hairs coming off of them in all directions. This bark makes an outstanding fire starter - it peels off very nicely without harming the vine.
The bark and wood of the sassafras tree burns quite well - I have found that the bark even burns well when moist from rain.
The leaves and dry twigs of the willow tree make for excellent tinder (but larger pieces of willow make for crappy firewood, so you know).
The fluff from a cattail, a pussy willow bush, or a milkweed plant all do an adequate job of catching your sparks and building them to small flames. Dandelion fluff from old dandelions works quite well to catch a spark and flame up - check out a video of dandelion fluff burning HERE.
Dead pine needles (dead pine needles are brown, not green) can often be coaxed into lighting from just a few sparks. Dried grasses and mosses often work even better.
Wood shavings created by whittling on a dry stick of virtually any tree will do an adequate job of catching fire from a match or lighter, but don't expect them to light from just a spark.
But It's Raining!
If it is especially damp you can get dry tinder by whittling away the bark from a dead branch and revealing the dry wood beneath. This wood can be shaved into a pile and should start from a match or lighter. Birch bark still lights fine when it's wet if you are fortunate enough to be near one.