Your "core" muscles are defined as those that wrap around your midsection. They include abdominals, obliques and spinal erectors. They serve many functions, including rotating your torso and supporting your thorax and back. Building these muscles up will help your performance in other exercises and improve your posture and balance.
Start with walking or jogging. If you don't normally exercise much, an added walk or short jog a few times weekly will strengthen your core muscles. A couple of miles each week will prepare your core for more advanced exercises.
Perform bodyweight core exercises at home. Experiment with exercises like the bridge, abdominal presses and sit-up variations. Basic sit-ups and crunches are easy: Lay on your back with your knees bent and feet on the floor. With your arms crossed over your chest, bring your chin up toward your pelvis as you tighten your abdominals. Perform an abdominal press by lying on your back. Bring one or both knees to your chest using your ab muscles, and attempt to push them away with your hands. Perform a bridge by lying on your back with your knees bent and feet flat on the floor. Bring your pelvis upwards so that your thighs and torso form a straight line. Hold for 3 seconds.
Swim to strengthen your core. Doing a few laps at a pool is a fantastic way to add core strength. Swim for 20 to 30 minutes for a great overall workout, both muscular and cardiovascular. Many gyms offer access to a pool as part of a membership.
Add strength training to your routine. Lift free weights or use weight machines two to three times per week. Start with light weights that you can easily perform 12 repetitions with. Add weight as necessary. Use dumbbells and free weights if you can--they are more effective at building your core because of the body stabilization involved. Compound lifts like pull-downs, pushups and bench press are better core builders than isolation lifts like arm curls, leg extensions, and calf raises. Many gyms have weight machines you can use to strengthen your abs and lower back. You also can perform core-specific exercises such as a dumbbell side bend, in which you stand with dumbbells at your sides, bend your waist to the left, then repeat on the right. (See Resource 2)
Perform bodyweight strength training exercises. If you are comfortable doing pullups, pushups, dips and squats, do them. Although they don't directly target core muscles, bodyweight exercises are among the best core builders because they require core stabilization against your body's entire weight. If you can't do bodyweight pullups or dips, start with negatives and slowly build your strength. For example, jump to grab the pullup bar and use the momentum to pull your chin over the bar. Then let yourself down as slowly as possible.
Play sports. Sports like soccer, tennis, baseball and racquetball are great core-builders. Join a local league or grab a racquet and play with a friend. This is a great way to build core strength while having fun.