Choose the item you wish to have autographed. You can get a regular autograph collecting book, a picture or poster of the star you are seeking a signature from, a giant tennis ball like the ones sold at some of the major tourneys, or even choose a spot on your body such as the back of your hand or your upper back.
Visit a tennis tournament. When you purchase your tickets for the event, consult with the folks on-site regarding whether there will be special autograph sessions. If not, don't despair there should be plenty of opportunities to get your player's John Hancock. Try to get tickets up front near the area where players will make their entrances and exits to and from the locker rooms. Stars often sign for fans following a match and you are most likely to get yours if you are in the most accessible place.
Stake out the practice courts before and during tournaments. The pros all practice and warm up for matches so you are likely to get close to them if you hang around the courts purposely set aside. Ask tournament workers for a copy of the practice schedules so you can get an idea of the time you can find your favorite. Wait until after the practice is finished to ask for your autograph.
Find out what hotel the players are staying at. Generally, most players stay in the same hotel and a little detective work can get you the information you need. Visit the hotel or even stay there is you are traveling to the tournament and hang around the lobby or hotel restaurant. Make sure you are not breaking any rules and stay away from players' rooms even if you do find out which ones they are. Remember to respect the pros personal space.
Look for promotional events featuring your players. These are often conducted by the stars' various sponsors. Contact the companies they represent to find out about planned promotions that involve autograph signing and to suggest such events for your area.
Write to the player whose autograph you desire and request an autograph. Often you can make contact with the star or at least those who work directly with him through an official website. You also might want to contact the ATP (Association of Tennis Professionals) for male players or the WTA (Women's Tennis Association) to make contact with a female player. Also, some fan websites may offer avenues for obtaining an elusive signature (see Resources below).
Search online auctions like eBay to buy autographed articles by the professional tennis player of your choice. Many times you can purchase signed photographs or posters from these venues. If you have the money you might want to bid on autographed personal items that players often donate to charities who auction off the items (see Resources below).
Check a player's tournament schedule through the ATP or WTA to find out when and where they will be traveling. Often you can make contact with a player who is leaving one event for another at the area's airport. The stars often have delays in their traveling like the rest of us and are likely to be receptive to signing a few autographs while waiting (see Resources below).