Getting started on a good lower back program is an excellent way to strengthen a large part of your core and also to ensure that you stay injury free for a long time to come.
There are a variety of different exercises you can include in a lower back program, some of which will also work other areas of the body. The best ones will include stiff legged deadlifts, supermans performed laying on the ground and then extensions.
Note that to perform extensions as part of your lower back program you will need to have a special piece of equipment at your gym where you can lock your legs into place and hang your upper body off the padding. If you don't have one of these, you could alternatively make your own version at home by laying off the end of the bed so the hips are at the very edge. Have someone hold your legs down (may work best if they actually sit on the lower leg) so that you do not fall forward. Then, lower your chest as close to the ground as possible and then rise up once again.
You should perform a workout that targets this area of the body once or twice a week, either combining it with the rest of your upper body training or dedicating the session to it solely alone. Aim to include about 1-2 exercises along with 1-2 exercises for the upper portion of your body. This would include things such as lat pull-downs, bent over rows, horizontal rows, shrugs and so on. With each exercise try and lift a weight where you are fatiguing within 8-12 reps if you are looking for muscular hypertrophy and 5-8 reps if you are looking for strength or power.
Finally don't forget to include stretching at the end as this is important to promote good recovery.