The other posts were fine, and may work for you. Excercises to strengthen your midsection are an especially good idea. But here is a classic piece of advice I always post when that question gets asked...
Raise Dat Stem!
by Bob Gordon
A flat back is one of the hallmarks of an experienced cyclist, particularly a racer, and over the years I have seen the prevailing attitudes towards rider positioning devolve to the point where if you don't cycle with your back parallel to the ground, you're cast off as a beginner.
But like many other concepts recreational riders adopt, the low back originated in the professional ranks after extensive research in aerodynamics proved this would help the fast go faster. Competitive athletes routinely sacrifice both their short and long term health for the express purpose of winning, but you may have a different agenda.
Lower back disc problems peak the ages of 30 and 50. There are many causes, but if your back pain is exacerbated by riding, it's a good bet the cause is bouncing around on your bike while your lower spine is extensively flexed (loss of lower back arch). A low, forward torso causes the inner portion of the disc (the nucleus purposes) to press back against the outer restraining fibers (the annulus fibroses). This pressure eventually causes the disc to bulge or herniate. The nearby nerves get squeezed, and the next thing you know, someone like me is telling you you have sciatica.
Cycling mitigates some of the problems of a habitually flexed lumbar spine because of the "bridge effect" that's created by resting some of your weight on your hands. But the lumbar region and its soft tissues are still at risk just by being continuously hyper flexed, and if you sit all day at your job, the danger is compounded.
On the flip side, cycling entirely upright does not solve the problem either. True, the inter-vertebral discs and spinal ligaments are in a more neutral position and absorb shock better, but the load is now transmitted axially, which is fatiguing and jarring. Also, in a bolt-upright position you can't use your gluteus or hamstrings to great advantage, which means your thighs (quadriceps) get overworked, you lose a lot of power, the unused hamstrings and gluteal muscles go flabby, and you catch all that wind. It's hard to be happy about all that, racer or no.
There is, however, a position that allows good performance while minimizing risk of lower back injury. I like a stem height and length that puts your back about 50 degrees from horizontal, while your arms and legs bend slightly at the elbows, as shown in figure 2 up there. To achieve this, you'll probably have to raise your bars, and assuming you want to keep the same bar style (as opposed to riding with stingray bars or something), that usually means getting another stem, one with a taller quill or a steep rise to it. If you hit the sweet spot, a photo of you from the side will reveal a nice pyramid composed of top tube, torso and arms.'