It really does depend on what county jail we are talking about. Contrary to what Mr. Blum reports, Travis County gives credit for any part of one day spent in Travis County Jail. For example, if you had two days to do and turned yourself in at 11PM and stayed in past midnight, you would be credited for 2 actual days.
I'd recommend talking to your attorney who represented you (or the jail itself) to get more specific information for the county you're going to serve time in.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.