Collecting autographs is an interesting hobby, with potentially little or no cost involved. Even very large collections take up very little space, especially if the collector files the collection in a photograph album. My preference is the 'slip in' sort. Certainly, do not glue them in!
Often, collections are themed - footballers, actors, musicians, politicians, and so on. Start with something you are interested in, and look out for opportunities. For example, footballers can usually be found around their home stadium on match days. Go early, or wait after the game, and this is a relatively easy "first collection". Buy a programme from the club shop (as they often have photographs of the players in there - for recognition), and try and get the autographs of all the current first team squad. You'll have a feeling of real satisfaction when you 'get them all', but do remember the trade in players means you'll soon need to go hunting again!
I suggest you buy a 'Sharpie' pen (by Papermate) from a stationery shop (W.H. Smith, perhaps), and some white blank postcards. Get one autograph on each card. Make a pencil note on the back of the name of the person who signed, plus the place where he/she signed and the date. Signed photographs or other pictures are nice too. Take them yourself, cut them from magazines, or buy them. I'd suggest 5" x 7" as the ideal size, and this is my personal preference.
Getting other items signed is also nice, but remember these take up more space. Footballs, shirts, books, programmes, magazines and so on are nice additions to a collection. Perhaps these larger items are best reserved for 'star players', 'star drivers' and others at the top of their professions.
When it comes to getting the autograph, these are my top three tips:
1. Be 100% polite. The celebrity does not have to sign for you, and a nice smile, a please and a thank you will help you (and other collectors in the future) a lot.
2. Be assertive. The celebrity often will sign for a few minutes, before (reasonably) heading home. If you wait too long for your turn, you may miss out.
3. Be patient. The celebrity may have meetings after their event, may wish to change or take a shower. However, they DO go home eventually and patience nearly always pays off.
Finally, be careful if you decide to add to your collection by purchasing autographs from others. The only sure way of knowing that an autograph is genuine is to be there and watching as it is signed. There are fakes galore out there, and if it looks too good to be true, it probably is. There are reputable autograph dealers, and collectors clubs (such as UACC) and these can provide you with extra assurance of authenticity. But if the celebrity is alive, it is still more fun to get it yourself!
Good luck in your collecting!