So if I have a frame, how do I know what size bottom bracket to get?

I assume if I measure the inner diameter of the bottom bracket shell (is that what it's called.. the hollow cylinder on the bike?), I should just buy a bottom bracket that is the same diameter... or should it be slightly less to allow it to fit?

And for width, do I just measure the width of the shell, or do I add/subtract a couple millimeters to determine the proper BB width?

Finally, what is the most common BB width and diameter; like is there a standard that most bikes seem to fit?