Check the artwork for any identifying marks that could tip you off about its artist. The most common methods of identifying the artist are signatures in the corner of a painting or on the back of its canvas, and etchings on the base of sculptures. It is important to attempt to identify the artist for the rest of the appraisal process.
Look online for other recent sales and purchases by the artist who made your work. The site Findartinfo.com is a very good resource for this step, as it allows you to search a large number of artists and artwork prices simply by searching by artist.
Search online auction sites like eBay.com for similar artworks, and try to find other auction records. According to ArtIC.edu, this will not earn you a professional appraisal as it is merely your own judgment, not that of a professional, but it is a good way to continue your search.
Take the work of art to an appraisal organization. There are numerous options to choose from in accomplishing this, including Tate.org.
Keep up to date with the appraisal. According to Art-collecting.com, an artwork's value can change quickly, and you will have to adjust your insurance coverage along with this fluctuation.