First off, OraQuick's plus is it gets significantly more people to test and one of the world's icons and best experts Tony Fauci, M.D. who runs Infectious Disease at NIH (and is a point guard on researching HIV cures, meds for early prevention, and vaccines has pointed this out). Right now 1/5 or 1/6 depending on whose series you read HIV I or HIV II (rarer and more atypical) patients don't know they have it, and potentially can spread it and deny themselves early treatment.

Home HIV tests are in drug stores or on line for about $40.
'
But be aware that there are drawbacks to OraQuick that Orasure who makes it doesn't want to advertise and you can do much better with a combo of "4th gen testing" like "p24"  and a followup RNA test or antibody test. Those cost more. So the ***windows*** that cause the virus to go down and then up can miss a diagnosis of HIV using the oral home testing swabs.  It's at home testing is analogous to home pregnancy tests. It's a mouth swab with results in 20-40 minutes.  
Home HIV test applications  to FDA began in 1987, and Orasure applied in 2005 for their two tests,  and got approved in 2012.

Downsides:

1) Oraquick is an ***antibody*** not an antigen or viral  test like some of the newer RNA/DNA or what CDC calls 4th gen tests, so it can miss HIV during the up to 3 months window when the virus can't be detected because antibodies haven't developed--and you miss a Dx of HIV.

Oraquick or other  rapid home tests made by Orasure are more accurate when done in professional labs.  The numbers are that home testing is 99.8% accurate when it's positive BUT 8% of the time it misses a diagnosis of HIV when it's negative because of the window before antibodies are detected. This is based on the infectious disease literature where many centers have tested it in significant numbers of people.

So 1/5000 using a test like Oraquick or the other oral home tests available, would get a false positive result, and 1/12 would get a false negative. So if you were to get a positive with an oral home test, you will be seeing an M.D. to do confirmation antigen (4th gen) and antibody testing and 1/12 people could miss a positive diagnosis.
_____________________
Early testing, Windows when testing is negative, & CDC's 6/14 Revised Testing Recs

On 6/26/14, the CDC announced new revised recommendations for testing that include "4th gen" tests like HIV-1 p-24 antigen or nucleic acid amplification test (NAAT) that can detect HIV as early as 3 weeks when viral loads are first high or peaking.  The problem with these tests is that after 3 weeks, "levels of p24 antigen fall as antibody develops and do not rise again until late in the course of HIV infection, it may only be detectable during a short window of time after exposure, so its utility is limited as an individual test."

To be certain that you don't have HIV, you're best off having 4th gen antigen testing 3 weeks or more after the possible exposure if you know when that was, plus later antibody testing or HIV-1 nucleic acid testing for resolution by an M.D.  The antibody tests are positive 2 weeks to 8 weeks much of the time, but there can be a window of up to 6 months before they are.

https://npin.cdc.gov/news/cdc-revises-hiv-testing-guidelines-better-id-early-cases

http://labtestsonline.org/understanding/analytes/p24/tab/test

http://www.cdc.gov/hiv/basics/testing.html

http://www.poz.com/articles/CDC_testing_protocol_761_25832.shtml

http://www.medscape.com/viewarticle/827473

RNA testing like PCR tests (polymerase chain reactions)(not done as a home test) are more expensive and the limitation of RNA or DNA testing alone, without antibody testing it alone is that it while they may be positive as early as ten days, they can become negative and you would need an antibody test 6-8 weeks or more after exposure (like ELISA or Western Blot testing, or HIV-1 nucleic acid testing for resolution per CDC's revised 6/14 one more accurate than oral home testing) 2-3 months or as long as 6 months later to confirm the diagnosis one way or the other.

Comparison RNA PCR / DNA PCR:

Another type of test is an RNA test, which detects the HIV virus directly. The time between HIV infection and RNA detection is 9-11 days. These tests, which are more costly and used less often than antibody tests

http://www.cdc.gov/hiv/topics/testing/resources/qa/be_tested.htm#wait

But RNA (viral loads) can become non-detectable in some  cases when the body finally fights back  .On the other hand PCR DNA tests are best used from 28 days on, but as early as 2 weeks, b/c these levels will not become none detectable over time