There are a limited number of artists' signatures available to browse for free on findartinfo.com website. Other than that you might want to get a subscription to a website such as artistssignatures.com which gives the option of buying a researcher's time. You can also browse their catalog of artists' signatures for an initial fee of around $10. Alternatively, you can buy, or borrow from a library, a reference book of artist's signatures.
Please bear in mind that not all paintings are by famous artists, or even by saleable artists. The vast majority of original work available on the second-hand market is either by unknown amateur artists or by artists whose renown has never extended beyond their local area. Picture research is very time-consuming and does not always yield results. Experts in this field justifiably charge a fee for their services, and you should expect to pay a reasonable sum if you engage the assistance of a researcher.