There are many ways to test your endurance, many mathematical equations that will give you a finite number that you then apply to your age, height, sex, and/or other parameters to estimate your current endurance level, threshold, or even V02 Max.
But if you cheated off the kid beside you in math class and if you aren't lucky enough to have a Sports Performance Lab at your disposal, then another less accurate, but informative way to get a gauge on your endurance is to do what you do best... Workout.
We all have our favorite workout. Maybe it is the 3 mile loop around your neighborhood, the 25 mile bike route that you and your friends do every Saturday, or the pool workout you throw throw together when your are pressed for time and need a quick workout to get the endorphins going.
The trick is to pick a workout that you know so well you could do it with your eyes closed. The next trick, and this is one that is a bit harder, is to make sure the workout you pick is one that you also have records of the total time it takes you to complete it and the average heart rate you performed those times at. If you don't have your heart rate info, the perceived effort information will also work (more info here)
Then, and this is probably the easiest part, go workout. Whether it is a 1000 yard swim, 24 mile bike, or 5k run, give it your best try and make a comparison to how you have performed in the past during the same exercise. Finally, take the difference in time, heart rate, or perceived effort and see how much you have improved, or declined, from your average attempts, understanding that changes in weather, diet, stress, and other factors can all negatively impact your results.
In summary, the least technical and maybe most important part to understanding your endurance levels is to pay attention to how you feel throughout your training so you can revisit various workouts to see if you have gotten faster and stronger then tweak your training if you need improvement or keep on going if you've seen an increase in your endurance!