The ideal is to leave yourself with grass that is about 2 1/2 inches tall after mowing. Each time you mow the grass, try to cut off only the top 1/3 of the grass blade. So do the math: the ideal grass mowing height is about 3 2/3 inches high (that is, this is the best time to mow).
So how do you remember this rule of thumb? And am I suggesting that you go out there with a tape measure to gauge the height of your lawn and determine when it's time to mow?
A little trick to make things easier on yourself is to draw a line across one of your lawn mower tires that stands 3 2/3 inches above surface level. Draw an arrow, as well, to indicate which direction is up/down. That way, when you think mowing time might be near, you can just wheel the mower out and see where the grass level stands in relation to your line.
As for achieving that ideal grass mowing height (at the end of the operation), initially you'll have to play around with the tire-adjustment mechanism on your mower. But once you've figured out what slot results in the mowing height you want (namely, leaving the grass at 2 1/2 inches tall), mark that slot so that you'll always know where it is.
Homeowners frequently cut warm season grasses a bit shorter; see cool season grasses vs. warm season grasses.
Research the various types of lawn movers on Consumer Search.