How to buy an authentic signature:

The best way is to buy an authentic signature from a reputable dealer like London's Fraser's Autographs. Or a sale that comes with a certificate of authenticity, checked by an official professional organization, like UACC, the Universal Autographic Collectors Club.
But sometimes, the signature may be passed on from a previous generation and hasn't any certifiable proof. Therefore you have to ask questions, like how the signature was obtained and by what circumstances, in order to check the seller out. The chance of getting a Judy Garland signature at £10 is impossible because most famous signatures range from £100 to £1000 pounds. If the deal is too good to be true, then most likely it's a fake.

On line site:

Have a look at what the seller has to sell. If he repeats selling the same signatures over and over again, then most likely he is forging them. Usually a fake seller only sells the most common/popular signatures, like Pop Groups or the 'in' Hollywood film stars. If the signature is signed in an autograph book, especially with a dedication, then most likely it is a genuine signature.

How to spot a fake signature:

The best way to check if a signature is real or not is to compare the signature with an official document, like a cheque. Having said that, signatures can be varied when signed under different circumstances. For example, in an event opening, the artist might sign his/her signature in a hurry, hence the signature will be more simplified from the signature signed in a less rushed situation. So buying a signature is a gamble, but it's fun. Just be wise... and happy hunting. You might find a treasure for life.