As much as people tend to want to get into advanced exercises as soon as possible, I firmly believe that high levels of core stability are required before you can even attempt to do some of the more basic ab exercises. I made this mistake for years when I was younger and had the chronic back pain to show for it. Core stability is actually often more important than core strength when it comes to preventing injuries and staying healthy. I highly recommend that everyone start with the following four isometric exercises done on a 6-7 time a week basis before they move into more dynamic exercises:
1) Plank aka Abdominal Bridge
2) Side Plank aka Side Bridge
3) Prone Mountain- Lie face down with your nose a couple inches off the ground. Extend your body as much as possible. With arms at your sides and palms up pull your shoulder blades back and down toward your feet. Keep your upper chest up off the floor and your knees and feet up off the floor by contracting your glutes and lower back.
4) Supine Bridge- Lie flat on your back with your heels 6-8 inches from your butt. Keep your arms at your sides, bend them 90 degrees and lift them up off the floor. Now raise your hips up so that only your feet and shoulder blades are in contact with the ground. Contract your glutes and push your shins forward throughout the duration of the static contraction.
Do one set of each, once per day. Try to work up to three minutes on every exercise but the side plank; two minutes is sufficient there. When you can do that your core stability will be dramatically improved, your lower back pain should be gone and you can now work into some more advanced ab exercises.