First, hand-write a letter to the player of your choice. You might want to do some research into a person's signing habits. For example, some players do NOT sign through the mail (TTM) at all. Others, even Hall of Famers do. There are forums on the internet, such as Sportscardforum.com that is free and has some addresses and recent successes. Just head to "Autograph Central" on there and you won't be disappointed.
The letter does not need to be long. Two quick paragraphs are all you need. Be polite, be quick, be courteous. ALWAYS say please and thank you.
Add your card or cards. NEVER expect a player to supply the card for you. In some cases they will send you their card and return your cards unsigned. This happens.
Add a Self-Addressed, Stamped Envelope (SASE). NEVER expect a player to supply postage or to write your address on an envelope. Your SASE should be smaller than your main envelope. I use 3 5/8" x 6 1/2" envelopes with the pull and seal. Some player don't want to lick envelopes if they don't have to. The envelope I use to send everything is the #10 envelope, or 4 1/8" x 9 1/2" envelopes.
Ok, so now you have your letter, your card, your SASE, and your envelope all made out. Double check to make sure you have the cards, postage and everything in order. Dump them in the main envelope, put in mailbox and wait.
The wait times for a return can range from less than a week to a little over a year. For novices I recommend sending to a stadium while that team is playing. For example, send to baseball players in summer, football players in fall, and basketball and hockey in winter. There are several sets, especially for baseball that are conducive to getting autographs. Topps makes a couple of sets such as their Heritage, Total, and Allen & Ginter sets. Many collectors like the look of an autograph on the Allen & Ginters. IT is a personal taste thing. A cheap alternative is the Topps Total. They are relatively inexpensive when compared to other cards, made of a good cardstock, and have a lot of players in each set. If you do get a glossy card, such as a base card from Upper Deck don't worry. Just rub it down with an eraser. Use one of those mechanical ones they sell in the pencil section of a drug store. They work great. Rub vigorously and you will notice the gloss just go away but the integrity of the photo will not be compromised.
Protecting your collection once you get it started is also very important. A binder and protective sheets works very well and is what I use. I have my collection in alphabetical order but you can do it by team or sport, whatever your heart desires.
So you're thinking, good players don't sign TTM. Why should I try? Well, I have gotten quite a few Hall of Famers back. Terry Bradshaw, Hank Aaron, Lawrence Taylor, Bob Feller (Required $10), Joba Chamberlain, Harry Carson, Antonio Pierce, Brandon Jacobs, Rodney Hampton, Robin Roberts, Bobby Shantz, Mark Grace, Sparky Anderson, John Wooden, Bobby Bonilla, Jim Thome, Jim McMahon, Gary Zimmerman, Dean Palmer, Richard Petty, Boomer Esiason, Joe Theismann, Dan Fouts, Fran Tarkenton, Tony LaRussa, Hank Blalock, Al Kaline ($5), Joe Dumars, Jason Giambi, Wade Boggs, Andy Pettitte, Greg Maddux, and Bob Griese are just a few of the guys I have gotten back. I have gotten almost 500 returns in a little over a year. Everyday I get mail and see a SASE in the pile it makes my day. You never know who its going to be.
If you are interested and I have not answered your questions here feel free to either email me or leave a comment, I'll get back to you. Hopefully, you'll give it a try. You can even ask me if a certain player signs and I'll let you know to the best of my ability. Happy hunting and may your mailboxes be full.