Porcelain is related to glass. When your sink was originally made, it either started on a cast iron or stamped steel base, got a vitrious finish sprayed on, and then was fired to fuse the coating together. Unless you happen to have a furnace that is big enough to take the piece qand get the temperature up to around 2000 degrees F, this is not a do it yourself project. Top quality refinishing requires major sand blasting equipment to prep the surface and spraying finishing materials that are extremely dangerous. You can't buy these materials.
There are many people out there who will be happy to just spray on polyester resin and tell you that your sink will last a lifetime--or at least until they change business names--whichever comes first. Therefore, you will really have to do some homework on a contractor to pick for this. You might check by searching the web, checking with architectural salvage yards and asking local home preservation groups for recommendations.