Starting Fire Without Matches
If you are a prepper, it's unlikely you'll ever get caught in a survival situation with no matches or a lighter on hand. These are essential items for any survival kit or bug-out bag and I'm sure you didn't "forget" to add them to yours. Even if your matches get wet or your lighter is broken or whatever other fire source you may have is compromised... you'll know exactly what to do to light a good, solid fire in any environment.
The first thing you need to know is this: you must have patience. It may last longer than you've initially considered, but you need to take your time, follow every step carefully and listen to your intuition. The second thing you need to consider is practice.
However, there is something you should ALWAYS have with you in a bug-out situation: a tinder ball.
Look for birch bark off a paper birch tree, dead pine branches, pine needles, dry grasses...
A tinder ball is, as you've probably figured out already, a ball (football size) made of tinder.
It should be tight enough to hold the scraps together, but not too tight, so the oxygen is free to circulate and keep the fire lit. It's light and it doesn't take a lot of room, but it will save you a lot of time when you need to start a fire. Just think of how much time you'd waste wandering around looking for tinder when you could focus on lighting the fire and keeping your family warm and protected.
A magnifying glass
STEP 1: Put together a "teepee" shape with sticks, leaving enough room for you to later place your burning tinder bundle underneath it. If possible, choose your sticks from a place other than the ground. If possible, it's best to use more than three sticks to make this structure.
STEP 2: Take your tinder bundle and your magnifying glass to your desired area.
Place your tinder bundle on the ground and then put your magnifying glass towards it, in an attempt to shine a small beam of light from the sun onto it.
STEP 3: Leave the magnifying glass in the same place for a minute or two, so that you can be sure you are creating an ember. The goal is to create a small, coal-like ember that will smoke on its own whenever you take the magnifying glass away. Your tinder bundle should start smoking a lot if you are blowing on it correctly and giving it the oxygen that it needs to create fire.
STEP 4: Gently place the tinder bundle that's on fire into your tee-pee structure so that it can start burning the larger sticks. To help the flame get taller and reach the larger sticks you should keep adding small little grass-like sticks to your fire to allow it to get bigger.
The Coke Can and Chocolate Bar
STEP 1: Polish the bottom of the soda can with the chocolate. Open up your bar of chocolate and start rubbing it on the bottom of the soda can.
STEP 2: After polishing the bottom of your can, what you have is essentially a parabolic mirror. Sunlight will reflect off the bottom of the can, forming a single focal point. Point the bottom of the can towards the sun. Place the tinder about an inch from the reflecting light's focal point. While I can't think of any time that I would be in the middle of nowhere with a can of Coke and chocolate bar, this method is still pretty cool.
The D-cell battery and gum wrapper method
STEP 1: The easiest way to do this is to fold the wrapper in half lengthwise, and use scissors to snip out a triangle from it. Let the triangle point come within a 1/16th of an inch of snipping the wrapper in two. If you do manage to accidentally clip it in two, it can still be used by manipulating the two sides of the wrapper to touch.
STEP 2: Connect the gum wrapper to the positive and negative terminals of the D cell and, within 30 seconds, you'll see an orange glow at the thinnest part of the foil bridge and then the flame itself.
Batteries and Steel Wool
STEP 1: Stretch out the Steel Wool. You want it to be about 6 inches long and a ½ inch wide.
STEP 2: Rub the battery on the steel wool. Hold the steel wool in one hand and the battery in the other. Any battery will do, but 9 volt batteries work best. Rub the side of the battery with the “contacts” on the wool. The wool will begin to glow and burn. Gently blow on it.
STEP 3: Transfer the burning wool to your tinder nest. The wool’s flame will extinguish quickly, so don’t waste any time.