There are a lot of variations of the depth perception tests used. The result is usually not dependent on the practice done by a patient. The results are based on whether both your eyes have a binocular vision or not.
The most commonly done is Random Dot 2 Stereo Acuity Test which uses polarized glasses. The test is composed by a 3 × 4 boxes grid, and in each row, three boxes contain a Symbol at a fixed disparity (500, 250 and 125 seconds of arc, respectively), and the fourth contains random dots only. Users must report for each box if they perceive an object at a different depth from the background, and they must identify the object shape. The shape can be a heart, hut, apple etc
The stereo acuity test is based on a graded circle test composed by 12 boxes, arranged in a 3 × 4 grid. In each box, three circles are depicted side by side, with only one circle placed differntly. The set of disparities ranges from 400 to 12.5 seconds of arc. The circles are drawn using a black and thick border. Starting with the largest disparity in a descending scale, the patient is asked to identify the circle at each level that appears closer than the others. The last level for which the subject answers correctly is considered to be the level of stereoacuity.
compensating vergence measures is done by the clinician. This is done by adding prism lenses on the trial frame for glasses and then measuring the amount of prism needed for each eye in the subject
Cover test is again done by the clinician by shining a torch in your eye and covering-uncovering each eye by turn to see any deviation present in either eye and if present how much is the deviation.
I am attaching photo of the random dot 2 test used for stereoactivity
Hope this information is helpful