I have a small collection of autographs - almost entirely of sports figures - which hold a prominent place in our basement (and which will hold a prominent place in my future basement, with Meaghan's blessing). I've gathered these in a variety of ways, from arriving early or staying late at sporting events, to writing letters, to attending signings. I'm not, however, the kind of person that winds up stalking across the country trying to gather autographs from the entire 1994 Toronto Blue Jays or something.
Although each autograph is special, each one feels a little bit different, depending on how it was acquired. As such, I've attempted to develop a classification system for the various autographs. Bear with me, if you will.
Stage 1 - Memorabilia
These are the types of autographs you buy in a memorabilia store or online. They come with a certificate of authenticity, and are often professionally prepared for display. The benefit to these is that it is guaranteed to be someone you like or admire, with the disadvantage being that you didn't get to meet them.
Stage 2 - The Appearance
You acquire these autographs at signing events, such as my Russell Peters one below. These may or may not be paid events (for Russell Peters, one had to purchase the book, but it was signed for free), and you may or may not be able to have a specific piece of personal memorabilia autographed. In these situations, you get to actually meet the object of your fandom, and may even get to exchange pleasantries with him, but you're often sharing that attention with several (hundred) other patrons.
Stage 2-1 - The Letter
These were once my sole means of autograph collection, because I didn't really realize there were other ways (or I couldn't afford them). In this stage, you've received an autograph by appealing directly to a player, via a letter (usually just sent to the arena at which the player plays). If you're blessed with time and patience, this can be a very effective (and cost-effective) manner in which to receive an autograph. There are several steps that can be taken to improve the odds of getting a reply, such as providing something to sign as well as a self-addressed stamped envelope, but I've had luck with a simple appeal (it might have been my 10-year-old charm, though).
Stage 3 - The Wait
This has been the most effective means of acquiring autographs for me, and has yielded some very unique ones - such as Arkells, Clay Guida, and Pinball Clemons, among others. This process is exceedingly simple - just get to the stadium early or wait after the game to try to catch someone's eye and score an autograph. You never know who you're going to get, but that's part of the fun. You might not get a word said to you, or even much eye contact, but there is something a little interesting about being only a few inches away from someone signing an autograph for you without a table in between you.
Those are my stages. Obviously there are autographs that may not fit into these. Where do you place a ball and hat that was waiting for you because you managed to get box seats at a baseball game? What about a hockey stick signed by Brian Leetch that some lady had in her car? Or, my best autograph, when your cousin gets his entire lacrosse team to sign a jersey for you. But not everyone is going to get those, and people are going to have other random ways they've collected those kinds of things.
Pictures to come, once I upload a few more.