What are common exercises to combat sciatica?

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.
"Superman!" As one who has a bulging disc (and no surgery), back strengthening exercises are very important to help stabilize the back. I recommend the "superman" exercise: lying on your stomach, stretch your arms out like you're flying through the air like superman. For 5 seconds, raise your right arm and shoulder, and left leg and hip off the floor, then repeat on the other side. Do this 12x on each side.