Deadlifts, backsquats and the press i.e. standing overhead press, NOT benchpress. You will inherently strengthen your back and core while performing these lifts as these areas (back and core) are required to maintain stability during the lifts.
If you have access to a gym, try doing lower back hyperextensions. Also, just as good is working on your core. Even doing simple planks will help that area out.
Deadlifts, backsquats and the press i.e. standing overhead press, NOT benchpress. You will inherently strengthen your back and core while performing these lifts as these areas (back and core) are required to maintain stability during the lifts.
Let me start by saying I am not a personal trainer and I do not have a medical background. That being said I am very active, in great shape and have spent tons of time working with trainers and researching proper techniques, etc.
Unless you are a body builder or professional weightlifter you probably don't need to focus on just one area of your body. You should create a weekly plan that gives you a good full body workout. You are far more likely to get hurt or injure yourself if you are focusing too heavily on one muscle group while ignoring it's counterparts.
So for your lower back, remember that having a strong core is just as important as having a strong lower back and in fact the two go hand in hand.
It is always a good idea to warm up before starting any type of exercise (especially your lower back) and remember to always start easy and give yourself plenty of recovery time. Now that that's out of the way, this site lists several great back exercises. I would take a look at each one, decide what your needs are and create a plan based on that. Just remember to start slow and practice good form - when starting any workout plan it's more important to have good quality form than to be killing yourself lifting too much.
Barbell - "Good Morning"
http://www.exrx.net/WeightExercises/Hamstrings/BBGoodMorning.html
Start off with a VERY LIGHT WEIGHT. This is a great exercise for your lower back, but like any back exercise, not one you should jump into. (Bruce Lee supposedly hurt his back trying to be a superhero during this exercise)
Another good exercise is what I call cat and camels. This video is a good demonstration:
http://www.youtube.com/watch?v=CXRsjICsGnc
The goal is to engage your core and keep your abs tight when doing this. By doing this exercise, you will ensure that your core muscles (back and front) all start to engage smoothly whenever you're performing any activities, and will help take care of any lower back pain due to tightness or muscle imbalances.
James V. has it right here... Ken does not. I do have medical experience, and I was a collegiate rower and then went on to row for the national team. Rowing requires a strong but flexible back, and serious back injuries are common and career ending.
All of the strength & conditioning coaches, and team physicians said that roman chair exercises (what back extensions are) are the worst things you can do to prevent injury. We did alot of cobra, superman, alternating bridge and medicine ball work.
The best thing you can do for your lower back is to strengthen your core. If you feel sore on your lower back, best to stretch it out with yoga. Dead lifting can injure your back if done incorrectly.
I'm with Michael Schaefer on this one. Deadlifts, standing military press and squats are your lower backs best friend. But if you happen to read this comment, for what specific reason are you looking to strengthen your lower back?
Hang from a chin up bar, raise your legs til they are parallel with the floor, hold then lower slowly, that's 1 rep. If this is too tough on your core and back, bend your knees. You can vary this by bringing your bent knees to a position where your thighs are parallel with the floor, hold this for 30-1:00 then rest/repeat. Also dead lifts, back extensions (lay on your stomach, raise your legs and your arms at the same time), and the key to strengthening lower back is CORE work. Your abs and your back at connected, if one is weak, both are weak.
In terms of directly accessing and building lower back strength, I've found that SLDL (straight leg dead lift) is a good addition to the general lifts. I'm a former football player (high school through freshman year of college) with experience in powerlifting and a number of years of personal training, both giving and receiving.
It's true that the core and back are built by the usual general exercises, but if you're looking to build lower back and core strength directly, in order to increase stability in other lifts, there are a number of muscle-group specific lifts that I've picked up.
SLDL is used for lower back strength training. Basically, using a barbell with low weight (until a comfortable level is evaluated) and maintaining an even, balanced grip on the bar with knees slightly bent to remove the use of the legs to force the weight up, keep your back straight and head up (looking upward is a useful trick to maintain form in terms of your back) slowly relax the bar towards the ground and then return to an upright position, maintaining good back form. This site includes a demonstration:
http://www.exrx.net/WeightExercises/Hamstrings/BBStraightLegDeadlift.html
The site is also a good resource in general, but it isn't as important as consulting with a professional in person.
Similarly, in terms of core weight training, the importance is to avoid focusing primarily on the upper abdominals (ie. crunches, situps, etc.) and build a general abdominal program. Lower abdominals can be targeted by leg lifts and knee or leg raises from a hanging position (as seen here: http://www.exrx.net/WeightExercises/RectusAbdominis/WtVerticalLegHipRaise.html
and here: http://www.exrx.net/WeightExercises/RectusAbdominis/BWVerticalLegHipRaisePB.html
as well as here:
http://www.exrx.net/WeightExercises/RectusAbdominis/WtHangingLegHipRaise.html).
The old standards are good, situps and crunches in their many forms, however they generally focus upon the upper abdominals, which creates an imbalance in the core.
The goal is to build a general core strength, which will allow greater support and stabilization for the other aspects of your workout as well as general health and comfort. The exercises above are a good starting point, but it's important to consult with a professional, in person, in order to gauge your starting point and the exercises which are best suited to you personally.
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I've known about the "Prone Cobra" for a while, and did a search to show you a video and actually turned out two more in one video - Prone Cobra, Superman, and Alternating Bridge: http://www.ehow.com/video_2351308_the-prone-cobra-superman-alternating.html