The solar system is full of debris which the Earth is continually encountering. Nearly all of this material burns up in the upper atmosphere, with nothing more than dust eventually reaching the ground. Nevertheless, perhaps 300,000 pieces of material survive to reach the ground every year, becoming meteorites. A few such falls are witnessed each year, and the meteorites are promptly recovered. In most cases, however, meteorites are found independently of a known fall, and may have lain on the ground for many years.
(Meteorites that are found after witnessed fireballs or directly observed hitting the ground are called falls; those that are found after they have fallen and aren't associated with any known fireball are called finds. Sometimes things fall from the sky that aren't meteorites, but are mistaken for them: debris from re-entering spacecraft, parts from aircraft, material flung from lawnmowers or nearby industrial equipment. Read my analysis of a fall purportedly captured by a camera back in 2004.)
Meteorites are roughly classified as stones, stony irons, and irons. Although stones make up 94% of all meteorites, irons are more commonly found. This is because they look more obviously different from normal terrestrial rocks and because they survive weathering processes much longer.
Look for meteorites in places where you don't usually find many stones. While there are as many meteorites in the mountains as there are on the plains, they are much easier to find if you don't have to visually separate them from thousands of other rocks. In many cases, meteorites may have already been found and gone unrecognized. In agricultural areas, look on the outside of fence lines, where farmers may have thrown them after striking them with their plows. Look also at the rock piles commonly used to weigh down corner posts of barb wire fences. Meteorites usually look "different" from other stones. It is quite common for them to end up sitting in someone's yard or rock garden because of this difference. Please remember that a meteorite legally belongs to the owner of the land where it is found. In the case of state or federal lands, you should contact the agency that administers the land (typically, the area ranger station.)
Iron meteorites often appear rusty, and are much heavier than ordinary rocks. They are usually irregular in shape, and often show pits or dents called thumb marks because of their resemblance to the patterns left by fingers in wet clay. Because they are an alloy of nickel and iron, they are strongly magnetic. If you grind or file away a bit of the surface, you will see that the interior consists of a white metal, possibly with tiny mineral inclusions. A material commonly mistaken for iron meteorites is slag, a by-product of the iron smelting process. Slag is often found along railroad lines, since many tons of it are hauled by trains. Unlike most iron meteorites, it is usually very dark colored and often shows a melted surface. Magnetite is a common iron ore that is magnetic and can be mistaken for an iron meteorite.
Stony meteorites are usually dark colored, varying from nearly black when freshly fallen to rusty brown for older, weathered examples. The outer surface consists of a fusion crust which appears quite different from the surface of ordinary stones. They are usually irregular in shape, with smooth or rounded corners. Like iron meteorites, they may carry thumb marks. Almost all stony meteorites have a much higher content of iron than normal rocks, and therefore feel unusually heavy for their size. If you file away a bit of the surface, you will most likely find that the interior resembles ordinary concrete, and will usually show shiny flecks of iron. Cinders and lava are often mistaken for meteorites, but true meteorites are much heavier and never show a porous or spongelike surface.