The most readily accepted documentation of birth data is obviously the birth certificate.  Although information included on the birth certificate varies according to when and where the document was issued, the birth time is frequently included.  If you have a copy of your birth certificate, that is the logical place to start your search.  

If you don't have a copy or the time isn't included, you may want to try this.  Check out www.vitalrec.com/ on the Internet.  This centrally coordinated site is connected with the health departments of all the states and allows on-line ordering of birth records (and sometimes death and marriage records for those of you interested in genealogy).  Just fill out the on-screen form for the state of birth.  Remember, if you have the choice of the "short form" or the 'long form" always select the long form.  When this version is available, it gives substantially more information than the short version. The charges vary by state but generally the cost of a certified birth certificate is about $5-20 plus postage.  Credit cards are accepted and can speed up the process.  A copy of the birth certificate is needed when getting a passport, so it's a good idea to obtain one if you don't already have a copy.

If the birth certificate is unavailable or does not include the birth time, all is not lost.  Often information included in a "baby book", family bible, or other historical family record may help.  In my own case, the Oklahoma birth certificate didn't list a time, but the birth announcement in my baby book did. 

Sometimes, especially in less populated areas, there may be an article or a notice in the local newspaper which may include the birth time.  If the archives of the regional newspaper are available, this may indeed prove helpful.

When the hospital where the birth took place is known, it is sometimes possible to get the information through hospital records.  Be forewarned however -- even when the records exist, hospitals often have strict rules regulating the release of this information.  Other times, the hospital may no longer be in existence, may have merged with another, etc.  Any of these situations further complicate the research. 

Less reliable -- but sometimes still quite helpful -- is word of mouth from your parents or others who may have been around at the time of your birth.  Just remember that memories tend to fade over the years and you may well get conflicting information.  But don't be too quick to discard this verbal information.  By knowing, even generally, when you were born is often a great help.  Non-specific times such as just before sunrise, before dinner, just after midnight...any of these may prove useful as we proceed to the next option.

If none of these methods have produced the birth time, another alternative remains.  Many astrologers offer rectification services.  By working with significant past events in the client's life it is often possible to extrapolate the birth time.  Fees for rectification service vary with individual astrologers and is often connected with the time expended in their work.  It is not uncommon to charge an additional 50% of the consultation fee if rectification is necessary.