How can you minimize the risk of leg clotting during surgery and recuperation?

Many options. After surgery it is standard to have leg stockings including pressure or pneumatic ones for preventing clots. Early walking and passive leg movements also help. In some cases use of blood thinners such as Heparin is preferred by doctors.
Lovenox, (enoxaparin) activity. Preoperative and postoperative anicoagulation, early return to activity, compression stockings and adequate hydration are the keys.
DVT prevention. Early ambulation (walking) can help. For high risk surgeries such as knee replacement and hip surgery, anti-coagulant medications (either injected or oral) may be recommended for a few weeks after the operation.