After you have exposed an image, the next step is to develop the film. Development happens either in a lab (which are dwindling in numbers) or can be done at home with some equipment and chemicals. With the right equipment, black and white film can be processed in broad daylight in about 15 minutes with three chemicals, so it's not terribly difficult.
Once the development has occurred, you have two choices. The first is to use the traditional printing method of using an enlarger to project the negative onto light sensitive paper. The more modern (and cheaper) method is to invest in a high quality scanner (I use the Epson V700) that can hold and scan negatives of all sizes, resulting in digital images that can be sent to a lab or your home printer.
Why are we doing this?
Right, that process sounded hard and cumbersome, but the end product is much more gratifying. I am left holding real images and the quality of these images is totally on me - from exposure to developing and scanning - the camera made no decisions. I find every film image far more gratifying than a digital image for that reason. There is also something very beautiful about film that digital cannot reproduce - and the quality of a nice film image is hard to replicate with digital.
Ok, what do I need?
Some film, a lens, and a camera. But we have decisions here...... what kind of subjects do you plan to shoot? Are you a color or black and white shooter? Do you want something compact, or are you okay hauling lots of equipment for a truly magnificent image? Finally, what size do you want your images to be? All of these factors make a big difference when selecting the gear and format to shoot. Let's look at the formats....
35mm (small) format film
This is the one you are probably most familiar with. It's what I saw my dad using and I briefly used as a kid. At one point there were even drive through film processing centers for 35mm! This size most closely matches the size of the digital camera sensor in a dSLR. The resulting image is about the size of a postage stamp, and is the smallest size most commonly used with photography.
Virtually every company has made a 35mm camera at some point - Nikon, Canon, Kodak, Minolta, Leica, etc etc etc. Many 35mm cameras also accept their modern lenses - I have a Nikon 35mm body that takes my "digital" lenses, meaning less gear to buy. If you need a body, eBay is flush with options. I paid $12 for my Nikon film body.....
The pros of 35mm are that it's the most readily available, it's the cheapest, there is an abundance of 35mm equipment on the market, and they are very compact and easy to carry. There are also tons of film choices in this category! The cons? It's smaller than the other formats, so the resulting image cannot be enlarged as much and "everyone does it." The larger formats certainly have a uniqueness and lure to them based on the rarer sizing....