1. Find the county that the individual was born in. Note: the county may have changed from the current county name. Example: Bexar county use to encompass most of Texas in the 1850's, so a large percentage of the 1800's birth certificates would be at the bexar county health department. So find the county that existed in the area of birth for your research.
2. If you can not get there in person, go to their website and see if you can order a copy online. Have done this many times before, it costs $$.
3. You can also pay someone in the area to look it up for you and get you a copy. Sometimes free, sometimes not. Go to a genealogy forum. www.genforum.com is a good one. Key in the last name of the individual and you can find many others researching the same surname and post a request there, you may find that someone already has a copy of the certificate and may share with you.
Hope this helps