How do you get rid of persistent swelling in one leg with the other leg being ok?

Compression stocking. Unilateral leg swelling can have several etiologies all of which are initially treated with a firm compression stocking during the day and off at night. Start with a 20-30mmhg gradient stocking and increase to 30-40 stocking if there is still swelling.
Need ultrasound. Lack of symmetry in leg swelling should first be evaluated by an ultrasound to assess the source of the problem. A clot found in a deep vein (DVT) would require blood thinners for at least 3 months since these clots can sometimes break off and travel to the lung. If no obvious abnormality can be found the problem can be addressed through leg elevation, compression stockings and maybe diuretics.
Compression stocking. It depends on the cause of the swelling. There are many different causes of swelling . If it is mild try compression stockings and elevation.
One leg swelling. Unilateral leg swelling requires an evaluation with including physical exam, venous ultrasound and, possibly, CT OR MR. Bilateral leg swelling is often times due to an underlying medical problems such as heart, kidneys, liver or lung. Unilateral swelling is usually related to something on the side of the swelling. See a vein specialist to begin an evaluation and start to wear compression hose.