Striking fire with flint and steel is not a difficult skill to master, but some basics of the method will make developing it easier. Five essential elements will be discussed, the flint and the steel, char, tinder and wood. After that, the method can be described.
MATERIALS
Flint Any piece of flint can be used, but flint of a good quality will make the job easier. The same clear black or gray flint used for gunflints is very good. It needs to be of a large enough size to be gripped tightly in the fingers so as to maintain control while striking the steel. Flakes of flint broken off a spall in making flint artifacts are excellent, as they usually already have a sharp edge and are of good size. The edge does not need to be razor sharp, but should be at least as sharp as a gunflint. The edge can be sharpened using either pressure or percussion flaking, just as the flint in the flintlock is treated.
Steel Any piece of good hard steel can be used, but the traditional steel is in the shape of a "C" with variations. It needs to be large enough to stick some fingers in for a good grip, again for control. Any correctly tempered high-carbon steel will work. Old files make excellent steels, and are frequently used for such.
Char Simply put, the traditional char is cloth that has been made into charcoal. It is heated at high temperature in the absence of oxygen to drive off flammable solids in the form of gas, leaving a black cloth which catches and holds a spark, smoldering with a hot ember rather than flaming. Making char cloth is not difficult. All you need is a can that won't melt in the fire, and some cloth. Anything from a lozenge box to a paint can makes a good can to start your char. The lid needs to fit tightly. Obtain a proper size can and punch a 1/16 inch hole in the lid. The best char cloth is made of heavy gauge cotton cloth, something like T-shirts, old towels, "terry" cloth and the like. Cut the cloth into squares of two inches, or so, and put them in the can loosely, not stacked tightly. Fill the can, but not so much as to compress the squares. Put the lid on and set the can in an open fire. I like to set it coals so it will be stable. As the can heats, you will see gases or smoke begin to stream from the hole in the lid. They may catch fire, from time to time. When smoke stops coming from the hole, drag the can off and let it cool. If you open it too quickly, the rush of oxygen will cause the cloth to burst into flame, and you'll have to start over. Once the cloth has cooled, examine it. Good char cloth is black, but still has a lot of strength. It should not fall apart from ordinary handling. If it's more like black ash than black cloth, you cooked it too much. If the squares are brown instead of black, or if it is obvious the cloth hasn't been heated evenly, put the top back on and cook it some more. Extra effort to make good char now will pay dividends when you put it to use.
Other substances than cloth can be used to make char. Punk wood that is in the process of rotting, but hasn't turned soft is very good. It can be broken with the fingers, but doesn't crumble. Standing dead tree with white fungus growing all over it, rotten enough to break, very light in weight, but still fairly firm. To make charred wood, the method is identical to that for making charred cloth. Break the wood into pieces from 1/2 inch to 1 inch, pile the can full, put the top on, and set it into the fire. Much more smoke comes from wood than from cloth, and that it's hard to cook it too long. (So much gas comes from the wood that it will push the lid off your can if it isn't pretty tight. Wrap a wire around your char can to make certain it stays closed, whenever cooking wood.) When it's right, it is black and as light as a feather. This stuff really catches and holds a spark well, and you cannot easily extinguish it once it catches.
Tinder Anything which will easily catch fire when exposed to the glowing char can be used as tinder, and many different things are used. Much of this depends upon the area of the country you live in, and what is available there. Flax tow, shredded hemp rope, dry grass, the list is long. Some have described using dry cattail down, but it burned up in a flash, much too quickly to serve well as tinder. Bark of a species of juniper tree known locally as the Red Cedar is very good. Strip bark from the tree, and it comes off in thin sheets one-half to one inch in width. Rubbing a bunch of this between the hands shreds it into a mess of very fine fibers, excellent for tinder. Keep this in well sealed plastic freezer bags at home, to make certain it is dry when needed.
Wood To catch the flame you worked hard to start, any small dry wood will work. Some whittle the side of a small limb to make a "brush", and that works well, but it is not necessary. Stacking small dry wood so it has plenty of breathing space, and in such a way that you can easily shove your flaming ball of tinder under it. Don't forget that on those wet days, dry kindling can frequently be found on standing dead trees.
METHOD
With all the materials assembled, we can now start the fire. There are two different ways used by the majority of people. In the first, and most common, the char, cloth or wood, is placed on the ground or some such suitable place, and sparks are struck with the flint and steel so that they fall on the char. In the other, all the materials are held in the hands. Both these methods will be discussed from the point of view of a right handed fire starter. Of course, wood for the fire has been collected, and the kindling is arranged to be ready for the flame when you produce it.
Dropping Sparks Pull out a bunch of your favorite tender about the size of an egg, flatten it, and lay it on the ground. Place a piece of char in the center of it. Holding the steel in your left hand and close over the char, grasp the flint in your right hand. Strike downward onto the face of the steel with the edge of the flint, causing a scraping, glancing blow at an angle of from 15 to 30 degrees, depending on the shape of your flint. This will knock sparks downward from the steel. The closer the steel is to the char, the hotter the sparks will be when they land on the char, and the better your chances. Once you see a spark catch in the char, and an area of red ember start developing in it, drop the flint and steel, wrap the char up into a bird's nest with the tinder, and begin to blow on it. No need to burst a lung, just steady blowing will do, and you can even wave it around instead of blowing. It will be good if you hold the nest above your head while blowing, as that will prevent all the smoke from blinding and choking you. Once the tinder bursts into flame, place it under your kindling and start thinking where the coffee pot is.
Hand-Held This method is a bit more difficult to describe, but works at least as well as the first, probably better. It's important to note that the flint and steel are held in the opposite hands to the first method, since the char is not below where the sparks originate, but above it. Make that same flattened egg of tinder. Select a piece of char cloth, and drape it over the flint in such a way that it lies on top of the flint, wraps over the cutting edge, and then goes under the flint. Hold the tinder in your left hand, palm up, and on the fingers, not the palm. Lay the char wrapped flint on the tinder, then grasp all the materials between the thumb and fingers of the left hand. You need to keep everything in place, but still have your thumb back far enough that you won't hit it with the steel. Now, holding the steel in your right hand, strike down at the edge of the flint at that same shaving angle. This means, of course, that the flint will cut through the char as it strikes the steel. That's what you want. You'll see that the sparks will be knocked off the steel above the flint---right where the char is. In a stroke or two, you'll see that a spark has caught in the char. Drop the flint and steel, wrap the char up into its nest of tinder, and proceed as before. This method is very fast in experienced hands, and easy and reliable enough that many smokers use it to light up their pipe. They simply leave out the tinder, and once a spark has caught in the char, place the char into the bowl of the pipe.