You can find an appraiser in your area by checking out the American Society of Appraisers or by contacting your insurance agent for a recommendation. An appraisal can be quite expensive so make sure you learn as much as you can before committing to one.
Remember that just because it is an original oil painting does not mean that it is valuable. You don't want to commit to an expensive appraisal if the painting is not worth much.
You can research your painting by checking out the artist's signature and looking for the name online. Also look at the back of the painting for clues. A gallery label may indicate some worth if it is a gallery that specializes in high-quality fine art. Numbers written on the back may show that the painting has been sold at auction. These clues mean that at some point in time the painting was good enough to be sold at an art marketplace. If that information is there, see if the seller is still in business. Contact them for information on the painting.
Collect any paperwork that you have about the art - receipts, bills of sale, letters, etc. If the painting is very valuable, you need to provide proof of ownership and a history of the work. This is called provenance which is documentation about a specific piece of art.