I understand your post to mean that you want to find the Local Mean Time of a birth or an event and you only have the time given in terms of the local time zone.
The easiest way to do it is to correct for GMT and find the longitude of the place where the birth or the event took place. For example, let's take a birth in Atlanta GA, at 10:00 am today. This time is recorded in EDT, which is 4 hours behind GMT. So the birth occurred at 14:00 GMT.
Now look at the longitude of Atlanta. It's 84 degrees 23 minutes West. For each 15 degrees West of GMT, time shifts back 1 hour. So 15 degrees West = 13:00, 30 degrees West = 12:00, 45 degrees West = 11:00 etc.
84 degrees West = 5.6 hours or 5 hours 36 minutes.
Which brings us back to 08:24 which is the approximate Local Solar Mean Time of birth. I've not allowed for the further 23 minutes of arc, which is just under half a degree or a 30th of an hour = 2 minutes of time.
That brings us to a more accurate 08:22 a.m. local time.
That's a bit long winded (LOL) but in practice it's 84/15 to get the hours difference for Atlanta. Don't forget the answer comes our as a decimal fraction so the .6 part is 6/10 of an hour = 36 mins
if you take a degree as being 4 minutes of time you won't go far wrong. A degree West takes off 4 minutes from GMT, a degree East adds 4 minutes to GMT.
Now if you know the longitude where EST/EDT begins, you can simply use that as your base and adjust your time by degrees difference.
The above calculation is obviously rough and ready but it is accurate enough for virtually all practical purposes and any astrology software will carry out a more accurate calculation simply by entering the EST/EDT time of birth.