Flint and Steel
By striking the sharp edge of a piece of flint or any other equally hard rock against a piece of high carbon steel, sparks can be made. The sparks must hit a "spark catcher", something that lights on fire easily when struck with sparks. Dry grass, the roots of dry grass, 000 steel wool, lint, charred cloth, or cotton balls are all good spark catchers. Often the spark catcher will start to glow and must be blown on before it bursts into flames. You do not need to use real flint to do this, nearly any rock that is as hard as flint will work. Many types of quartz, which is very common, can do an excellent job.
A little rod of mirth metal often confused with flint and steel. The mirth metal rod can be scraped with any piece of hard metal to produce extremely hot sparks. Little bits of the mirth metal can also be shaved off into a pile on the surface of whatever will be lit on fire. Some mirth metal rods are accompanied by a rod of magnesium that can be scraped to form a even better pile of highly flammable flakes. This method is much easier to use than the flint and steel.
Fire by Friction
There are many methods for making fire by "rubbing two sticks together". The most popular way is by making a bow and wrapping the bowstring around a stick. By making a sawing motion with the bow, the stick will spin back and forth, this can be used in a drilling motion on a baseplate of soft wood that will get really hot and throw off glowing embers if you move the drill fast enough. It is pretty hard to do.
Battery and Steel Wool or Thin Wire
If you simply touch the ends of a nine volt battery to a piece of 000 steel wool it will start to glow red hot almost immediately. You can put some tinder on top of this and blow on it to make a fire. Many variations of this are possible, perhaps even with a cell phone battery. This method is very easy.
By focusing the rays of the sun on a pile of dry leaves, grass, or grass roots, a fire can be started. Much like flint and steel, it may start to glow first and blowing on it will be necessary to get it to burst into flames. While it is easy to char things with a magnifying glass, and even make them smoke, it can be quite difficult to get them to actually light on fire.