Buying an autograph of a famous athlete or celebrity on ebay can be the easiest and most economical choice available. BUT, there are many factors to consider before bidding.

Is is real?  A better question maybe how can you know for sure the autograph is real?

There are many things to consider here:

a) Sellers feedback rating. Have they sold autographs before?
b) How is the autograph authenticated?  We've all seen the auctions "Comes with Certificate of Authenticity."  The fact is, that COA could easily have been printed on the sellers home computor.  Many big companies (Upper Deck/UDA, TriStar, PSA/DNA, Steiner) offer a serial numbered hologram on the actual autograhed item, that can be accessed on an internet database found on the companies website. Good sellers will list this serial number so you can go to the companies website and indeed check if that autographed item is in the database.
c) Who is the best?  There are many good companies, I personally like UDA/Upper Deck, PSA/DNA, and Steiner. 
d) What if the autograph does not come from a big company? Be very weary of 'mom and pop' authenticators. There are many ebay sellers who will put an autograph up for auction that they "got signed in person."  It boils down to a simple matter of whether or not you believe the seller. There are sellers who make a life out of tracking down athletes and famous people, get their autograph, and put it on ebay. And the only COA is the sellers word. I've seen those sellers. And to be honest I would buy from a seller like that. Who had a track record of selling autographs. BUT, those sellers are few and far between. 

Some helpful tips:

When looking for that famous sports star autograph, why not buy an autographed card? Virtually all the big stars will sign for Topps and Upper Deck and appear in many sets throughout the year. These autographed cards can be found on ebay, often times for far less then an autographed ball or jersey might sell for. Also, you know the autographs are real! These companies have a huge amount of interest at stake in making sure that the cards are indeed authentic. Imagine if it turned out that some of the LeBron James 2003/04 SPx Rookie Cards were fake autographs? Wow, Upper Deck would have a public relations nightmare.  It would be HUGE hobby news and could have serious negative ramifications. Upper Deck and Topps take great care in making sure that these cards are indeed signed by the player and often times have company representives witnessing the autogaphs sessions themselves.

Some athletes have exclusive autographed deals. For example, Lebron James, Michael Jordan, Tiger Woods and Kobe Bryant all have exclusive deals with Upper Deck. Meaning you won't find any current James, Bryant or Jordan autographs coming out of a Topps product. Also, be carefull when you find an autographed ball or jersey of one of these players and it's NOT authenticated by UDA.  Jordan, James, and Woods have had long-term deals with U.D. and I would stay away from items that are not UDA.

I really like PSA/DNA.  PSA is very popular in the grading card market, and their autograph authentication service is excellent. For as little as $10.00 you can send in your autograph and have PSA/DNA's experts determine if it's real or not. I would 100% buy a PSA/DNA authenticated item on ebay. If you are selling an autograph, why not take the extra time and get a PSA/DNA COA?  Esspecially if it's a big name in the sports/entertainment industry. If you're selling you're "grampa's Mickey Mantle autographed baseball" you'd be a fool not to get PSA/DNA to look at it first and authenticate it for you.

Helpful search tips. I like to search using psa/dna and uda.  Just do a search of 'psa/dna autograph' and you'll see some really neat stuff.  I like also using the word 'autographed' in the search feature because some sellers use it instead of autograph, or auto.

Hope some of these tips were helpful.