It varies depending on several factors: whether it is a partial or total eclipse, how close the moon is to the earth in its elliptical orbit (this affects the apparent size and speed of the moon), how close the earth is to the sun in its orbit (this affects the apparent size of the sun), etc. In general, though, a total eclipse takes on the order of a couple of hours from start to finish, with totality (the part where the sun is completely blocked out) on the order of a couple of minutes.
It's actually pretty easy to estimate the first number - all you have to know is the apparent angular size of the sun and moon in the sky (about half a degree each) and the the time it takes the moon to orbit the earth (about one month). I'll explain how to do that in the next paragraph, but you can think about it yourself beforehand if you want...
[Answer: the entire disk of the moon (half a degree) has to move across the entire disk of the sun (half a degree), so the moon has to move one degree with respect to the sun between the start and end of the eclipse. One degree is 1/360 of the way around a circle and therefore 1/360 of the moon's orbit around the earth. 1/360 of one month is on the order of a couple hours.]
This page was last updated June 28, 2015.