Here are a few  ways to research autographs;

 Most authors have their signature on their websites which makes it easier for  collectors to recognize a fake.  There are many fakes floating around sites such as ebay. Some authors even address this with a statement on his/her website.

If you are buying a book signed by a president or a political figure, the signature can be found on their official website or on a Web encyclopedia such as Wikipedia. 

And of course you can compare to other listings on ebay.

Note that signatures do vary, no one signs their name exactly the same every time , there will almost allways be some slight differences,  and some authors have multiple ways of signing their names.  They can also change with the persons age.

Forgerys can be  very good  and it may be difficult to detect the work of a pro.  It helps to get to know the dealers from whom you purchase.   

Publications like the Pen and Quill, which publish the work of known forgers.

But in the end, no matter how much exsperience you have,  the only true way of knowing a signature is real, is to be there when it is signed.