Poor sleep is one of the most common complaints after a knee replacement - and it usually improves as the knee settles.
Positions that work for most people: on your back, or on your side with a pillow between the knees. Avoid keeping a pillow under the knee for long periods - it is comfortable, but it keeps the knee bent, and regaining full straightening matters for how you will walk.
During the day, balance activity and rest: short walks and exercise sessions spread across the day beat one exhausting effort followed by hours on the sofa.