Sit on the seat and put the HEEL of one foot on a pedal. Rotate the pedal until it is in the six o'clock position. If the seat height is about correct, your leg should be straight with you sitting normally on the seat. When you move your foot to put the BALL on the pedal, there will be a slight bend in your knee.
You may have varying things going on because of your knee replacements, but generally, you may need to adjust the seat up or down in tiny increments (millimetres) to achieve the optimum position. Indicators are that if you get pain in the back of your knees, the seat is too high. If you get pain in the front, the seat is too low. If you get pain in the side (illiotibial band) you are pushing too high a gear.
One caveat, however... most people have one leg longer than the other. The fit method used above has actually allowed me to identify this with some without them actually telling me. If your legs are different in length, you may need to consider orthotics on one side.
With the seat adjusted as above, it is likely that you will be balancing the bike vertically between your legs, but be on tippy-toes. If this is a problem, tilt the bike over on your favoured side.
For most off-the-shelf seats, your seat should be horizontal to start off with. However, slight adjustment of the nose up or down (by millimetres if your seat clamp will allow it) is permissable to relive pressure on the perineum.
There is another adjustment which relates the front of the knee to the pedal spindle when a crank is horizontal, but we might leave that one alone as it relates more to frame size and TT length.
We deal extensively with these fit issues in the courses we run.