How much is best to walk when you have a very swollen leg?

Depends: The cause of the swelling dictates the activity level. For some causes it is no activity - like a blood clot. For simple causes the more the better.

Get it checked: You need to have your leg checked for why it is so swollen. Different causes have differing treatments, so i'm not going to suggest a treatment without knowing the cause. Unilateral leg swelling can have benign causes, but some causes can be life threatening, so get it checked.

Swollen leg: Firstly, it is important to determine the source of the swollen leg. If this is result of an infection then leg elevation would be important. If this is a more chronic condition then use of a compression stocking would be very helpful and then there would be no reason not to be walking.