I found this website to look at the sky at the specific time and location: http://www.fourmilab.ch/cgi-bin/Yoursky - you can insert latitude and longitude and time to see how the skies looked at any location/time. What I need to find out is when a particular constellation reached its zenith. I see that if I change the Universal time the location of the constellation in the sky changes, but where is the zenith of a constellation? The constellation in the question is Bootes. How do I know its zenith time let's say for today? preferably using the website above.
The key number you need to find is the "right ascension" This tell you the "longitude" of the constellation, relative to the other stars in the sky. It is measured in hours and minutes
Bootes has a right ascention of about 14:30 This means that on the day of the spring equinox (March 21) it will culminate at 02:30 (in local solar time, you'll need to make adjustments for daylight saving time or if your local noon isn't at 12:00) Note that 14:30 is 2:30 pm
Every month it will culminate two hours earlier So on April 21 it will culminate at about 00:30 (conveniently there are 12 months and 24 hours)
Working the other way, On January 21st it would culminate four hours later, or at about 06:30, and now, in Early February it culminates at about 06:00
This kind of calculation is good enough for a rough estimate. More accurate calculations can be done, but are more convenient to get a computer to do them.