The best way to measure results is usually by comparing tests administered before surgery to values for the same tests re-administered after surgery. This information can come from before and after X-rays, range-of-motion, and strength testing.
Some facilities (usually at a university clinic or hospital setting) are set up to conduct gait analysis. The patient walks along a platform or special floor that has force plates built into it. A video camera records your movements from all sides.
Using this type of video data and computer software analysis, it is possible to see what kind of weight-bearing pattern you may have and how it changes from before to after treatment.
Without this more specialized testing, there are several well-known tests (e.g., Lysholm knee scale, Hospital for Special Surgery knee rating system) that can be used to assess symptoms, function, motion, strength, deformity, and stability. Your surgeon or physical therapist will help you complete these tests. By repeating the tests after a set period of time (e.g., every month), you will be able to see measurable results.
Of course, using a more casual approach is also possible. You can keep track of how many steps you take each day or how long it takes you to get up and down a set of steps in your home for example.
You can also keep a log of knee motion by measuring how close you can bring your heel toward your buttock when lying down (hip and knee bent, foot flat on the floor, slide heel toward your bottom). Use a ruler to measure the distance between heel and bottom.
There are many other ways you can gauge your own progress if you think about measuring any aspect of your daily activities and exercises. Think in terms of time, distance, number of repetitions, and so on.