In the most basic way, film photography is the process by which light is recorded onto a cellulose and silver media. Light passes through a lens [note the number and type of lenses are diverse] is focused therein, and finally collides with an object that has been made sensitive to light, and until the point of photographic exposure, protected from any contact with it.
There are as wide a variety of film medium as there are digital cameras, ranging from small format [aps and 35mm] to medium format [120 or 6cmx6cm] and even large format [up to as large as 11x17 inch film]. Similarly, the way in which those media are housed [camera types] are equally as diverse.
To get into the field, it is easiest to start with 35mm negative film. This is the standard form for film photography, and is easiest to have developed. Often with 35mm film you get 36 frames, although 24 is more common in standard film stock from the store. There are color and black and white films, as well as black and white films that can be processed in color (C-41) chemicals, giving a black and white look with a greater range of options for development. Black and white film can be developed at home with certain chemicals (black and white chemistry is less sensitive to temperature as color chemistry, which requires constant high temperatures) or also sent out to a lab, but there are a limited amount that will do this.
There is also slide film, or positive film, which creates the image directly as taken in the camera onto the film. These are mainly used for projections, and can also be scanned using a negative scanner. Making prints from them is a much harder task than with a negative film, but the results can be striking. Often with color slides there is an increased saturation and/or vibrancy of colors. These films will also need to be sent out to a specialty lab, although they can be cross processed as well, meaning they would be developed as if they were negatives, leading to wild color shifts and increased grain. This is harder to do at a standard drug store lab, since they fear that it will ruin their chemistry, but it has very little effect on it. The slide film is then a negative film, and can be used to make prints.
These film types also apply to medium format or 120mm film. These are for older cameras, and provide much larger negatives, and thus less magnification is needed for enlargements resulting in better quality. Medium format cameras use 120mm or 220mm film (220mm film is a double length roll of 120 film - paper leaders - 120mm film has a paper backing the entire length of the roll. Formats of medium format cameras are (Fuji/Bronica/Contax/Pentax/Mamiya/Holga) 6x6.45cm resulting in 15 frames, 6x6cm resulting in 12 frames is the most common, 6x7cm for 10 frames, then the less common 6x9cm, 6x12cm and 6x17cm are the other medium formats. This type of film will also need to be sent to a specialty lab, although your drug store or grocery store can send these out to a local fuji lab or it can be hand processed at home with a temperature controlled water bath. Black and white negative film can also be developed at home or in a group lab.