Find a stronghold without wasting Eyes of Ender! Instructions below.
Write your coordinates in Initial X and Initial Z. Throw the eye of ender and place yourself right under it when it's hovering in the air. Write your new coordinates in Final X and Final Z and press Add measurement.
You'll get an estimate of the Stronghold's position as soon as you have two measurements. In order to improve its accuracy, you should take your measurements far away from each other. After taking the first measurement, move several hundred blocks to either side. This prevents bearings which are close to parallel (bad for estimation). Taking additional measurements also improves accuracy.
Each time you throw an Eye of Ender, the game is telling you that the Stronghold is somewhere on a line that passes through the throwing point and the landing point. So if you throw twice, from different locations, you know the Stronghold is in the intersection of those two lines.
However, there is a certain amount of error associated with each measurement. To combat this, you can take more than two measurements, which makes errors tend to cancel out. Since three or more lines don't usually intersect in a single point, the assistant looks for the point which is closest to all of the lines. It does this using a mathematical technique called Linear Least Squares