How do you exercise after a foot amputation?

Modify. You may have to modify your routine exercise. There will be certain limitation to consider. You want to avoid anything that causes further breakdown of your skin, leading to ulceration and further infections and amputations. Shoe modification is also very important.Depending on the level of the amp, you may need fillers to help. Also ask your doctor if any work is going to be done on your achilles.
PT can help. It really helps to work with a pt familiar with amputees. Effort, optimism and support will be essential as you first start walking with a prosthesis. Exercise is needed to strengthen arms and legs and improve balance and stability. As you probably know, there are many famous athletes with amputations who compete in marathons, biking, skiing and swimming. (see www.Activeamp.Org).
PT / Rehab. After the surgical site from the amputation site is fully healed, consult with a physical therapist or with a rehabilitation specialist and go over the exercise options that are best for you.