I'm still sort of astounded that your surgeon thinks you can rehab this on your own ... but whatever ...
I'm going to give you some basic starter exercises. When they become a piece of cake in a week or so, let me know (PM or email) and I'll advance them.
OK ... first lets do some range of motion exercises to get the joint moving well again. This will help with any residual swelling etc.
1. Wall slides: Lie on your back with your butt up against a wall and your legs up the wall (or in a doorway with just the involved leg up the wall and the other stretched out through the doorway). Bend the involved knee and let your foot slide down the wall as close to your butt as you can get it. Hold for 20 seconds or so and then straighten it by sliding your foot along the wall again. Repeat 10 or so times.
2. Supine towel slides: Sitting with your leg out straight in front of you, wrap a towel over your foot and grasp both ends. Pull on the towel and slide your heel toward your butt. Again, hold for 20 seconds or so and repeat 10 times.
3. Prone knee stretch: Take a towel (or you might need a sheet for this one) and wrap it around your foot. Roll over onto your belly and pull the sheet over your shoulders. Keep pulling until your knee won't bend any more and you feel a stretch in your quad. Hold 20 seconds or so and repeat 10 times.
I'll find or make pictures if these descriptions don't make any sense. Just let me know ...
OK, so now for getting your quads going ... this will be easy to start.
1. Straight leg raises: Lie on your back, and keeping your knee locked straight, lift it in the air about 24 inches. Pause, and slowly lower. Work up to 3 sets of 20 reps.
2. Short arc quads: On your back again, place a full paper towel roll under your knee (or a foam roller if you have one). Lift your foot up, squeezing your quad, until your knee is straight. Pause for several seconds, then slowly lower. Work up to 3 sets of 20 reps.
And now for the glutes and hamstrings ...
1. Bridging: Start with two-leg and progress to one-leg (when you get here, do them on each leg). Lift high ... and hold at the top for a good 10 seconds. 10 reps. 3 sets.
2. Clamshell: Lie on your side with both knees bent (doesn't matter which side because you are going to do both). Keeping your feet together, lift the top knee toward the ceiling. Keep your pelvis vertical and prevent it from rolling backward (so the movement is isolated at your glutes and hip). Work up to 3 sets of 20 each.
3. Single leg balancing. Balance on the involved foot on a firm uncarpeted surface. Hold for one minute. Do whatever compensation you need to stay upright, but don't fall over. If you can't do one minute, work up to it. We'll be doing a lot of single leg exercises in the future and we want your glutes and other stabilizers really working properly.
You can do all of these daily. Especially the stretching. In a week, we'll advance. Keep me posted.