To gauge where you stand, the easiest method--or rather the simplest, since push-ups aren't easy--is to continuously repeat push-ups without stopping until you cannot complete another without rest.
Another method is to set a time limit, and see how many push-ups you can complete, with brief rest in the up-position allowed, during the time period. This type of testing is usually done--as by the U.S. Army--over a two-minute interval and then compared to the charts and is a good measurement of overall strength.
Produce the Results
The first step is to get down and do the work so you can test your results.
According to the American College of Sports medicine, when doing a push-up, you should begin flat on the floor with your hands slightly wider than your shoulders and keep your toes (or knee, if you're performing modified push-ups, often used to test female performance) in contact with the floor at all times. Keeping your back straight, push up to the point just before your elbows lock, and during the down phase, allow your chin to touch the floor but not your stomach.
Continue either until you cannot do another push-up, or until your two-minute timer (if you're testing yourself against the Army stats) expires. Make a note of the number of push-ups you've completed.
Where You Stand
Using "The Washington Post" chart as reference, if you performed push-ups until you couldn't do any more (no time limit), you can see where you stand.
For women between 20 and 29 years old, a result of 21 to 42 full body push- ups or 30 to 45 modified will fall in the range of Fair, Good, Excellent or Superior--above average. If you're female and 40 to 49 years old, this range falls to between 13 to 20 full body push-ups and 18 to 33 modified.
Men between 20 to 29 need to complete 37 to 62 full-body push-ups to fall into the range of Good, Excellent to Superior, with the number of push-ups decreasing to 24 to 40 for 40 to 49 years old. To find out exactly where you place, follow the link to the "Washington Post" study below.
The Army's results chart for the two-minute time trial are bit more demanding, being held to a military standard, so after referencing their chart in the link below, don't worry if your results aren't where you want them to be. In fact, you will also find a valuable resource on increasing the amount of push-ups you are able to do.