Building a fire is one of those that can and will determine the outcome of a survival situation. With so much riding on the ability to start a fire, it makes tons of sense to plan and build a fire making kit. It is super easy and a little bit of fun to make with hundreds of options and skills to learn. You probably already have everything that you need sitting around the house right now. For this kit there are only going to be 3 basic parts that you will need, a container, the heat/ignition source, and finally the fuel. For the last 2 items your going to want to make sure that you have several different ignition sources and several different fuels.
For the container, it can be anything that is watertight and easily transported. This can be a small pelican case or a plastic bottle, even a ziplock freezer bag. Bear Grills has some pretty small ones that are nice to carry in your EDC bags.
For an ignition source, the minimum you should have a lighter, box of matches, and a ferrocerium rod. The lighter is a good go to item. It could be difficult to use in wind so a jet lighter would be a better option. I can also be used to dry out tender and kindling. Matches are nice but in most situations a lighter would be better. Spending the little extra for strike anywhere is a good idea as well, and if needed the match sticks can double as kindling. lastly the ferrocerium rod is an indestructible backup ignition source. It will take a lot more practice and patience then the lighter and matches and might be able to catch as much on fire but is the best back up option you will have.
For the fuel, dryer lint and cotton balls are perfect. (if you dip them in wax and break in half when its time to light will burn slowly). A candle is a good idea to have as a source of fire and light. Adding petroleum jelly to the cotton will help it burn slower and could double as a first aid item. Just have to be careful because in the summer the jelly will melt and can ruin a lot of the other fire starters and ignition sources.