There are two types of HIV tests. The most commonly used in an antibody test, which looks for the presence of antibodies that your body creates against the HIV virus. These antibodies may not show up for several weeks to a few months following infection however. The rapid tests, which can often be done orally, are antibody tests. To get antibody testing, see this site.
The other kind of test looks for the HIV virus itself (often called an HIV RNA or viral load test). This test will become positive shortly after infection, so it is an important tool for diagnosing those who have become infected with HIV very recently. If you have reason to think you might be very newly infected with HIV (check out a list of common symptoms of acute infection), you can contact the Primary Infection Clinic for possible HIV RNA testing or go to the Public Health STD Clinic at Harborview Medical Center and tell you are concerned about acute HIV infection.