What do I do for sciatica pain that is running down my leg?

It depends. Sciatica without numbness, weakness, or bowel or bladder symptoms is often treated with anti-inflammatory medicine like ibuprofen. It is best to avoid activities which can irritate the back like bending, lifting, pushing, pulling, twisting. Walking is usually ok if it doesn't make the pain worse. If the pain is severe, or persists for several weeks, or has other symptoms, it should be evaluated.
Core Exercises. Typically core strengthening exercises are the best to help relieve pressure and forces in the spine. I would try and google some or look them up on youtube to see descriptions. If you can do them yourself, wonderful otherwise ask your doctor to get a referral to a good physical therapist for further assistance.
LAST RESORT. If you fail conservative treatments rest, nsaids, physical therapy and steroid injections I would recommend seeing a spine surgeon who specializes in minimally invasive endoscopic spine surgery since surgery is done through small incision the size of your finger nail through a tube the size of a pen causing less pain and quicker recovery.