Is it better to try to walk around with sciatica or just rest?

Move with sciatica. Sciatica, pain radiating from your low back/buttock to your leg is usually transient. Although recommended in the past, prolonged bed rest is now discouraged. Although sciatic pain refers to pain from a compressed sciatic nerve which would result in pain down into your foot, it frequently doesn't go down that far; the pain is often caused by muscle strain.
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.
Most get better! This depends on the cause of the sciatica but typically, if due to nerve compression from a disc herniation, 90% get betternon operatively. All bets are off if you: smoke, are obese and/or don't exercise routinely. Short term rest and activity modification followed by exercise including walking is ideal. More than 1-2 days of rest should be avoided.