Step 1: Get a good quality, highly adjustable chair. Lumbar and height adjustments to fit your body are a must. Set your chair to perfectly mimick the natural curves in your lower back, and sit leaning back about 15-25 degrees from upright, with both feet square on the ground in front of you. Don't slouch! Lower the armrests so you can't use them... slouching to the side is tempting and is terrible for your spinal health in the long term. Your monitor screen should be positioned directly in front of you at eye level so you don't have to strain your neck at all.
Step 2: Stand up and stretch your legs, back, and neck at least once every two hours. I also like to go for a short walk around the office.
Step 3: Do core strengthening for your lower back 2-3 times per week. It doesn't need to be a complicated ordeal; light calisthenics for 10 minutes will keep you in much better shape than no exercise at all. Bridges, supermans, leg raises, and crunches all factor into my routine, and there are many variations on each so I like to switch it up. My only equipment is one of those inflatable exercise balls. You may want to visit a professional physical therapist to ensure you are getting the most out of your workouts.
Following something like the above plan is almost necessary for anyone sitting long hours in front of a screen each day. For me, with my tall narrow body shape, it is doubly so. I manage to get by with minimal discomfort using this plan. If I get lazy for a few months, sit slouchy and neglect the exercise, I pay with constant discomfort. The difference is huge.