There are many exercises you can do from home to build strength. Let's assume that you do not have any weight equipment and you want to start building muscle. It would behoove you to buy a chin-up bar, expander cables and a hand gripper. You could probably get by without the latter two initially, but the chin-up bar will be important for building back strength.
The exercises below are free-hand and calisthenic exercises. They are performed without dumbbells or barbells. Free-hand exercises are a great way to start adding strength and building muscle. They are easier on the joints and can be done at your convenience, even while you are on vacation. Some weightlifters started out with free-hand resistance training. It gradually accustoms the body to exercise, unlike bulky weights which can make you extremely sore for awhile. Joe Weider introduced his "7-Lesson Bodybuilder Course" in the 1950s, which millions have used to gain strength.
Try to do three sets of 10 repetitions for each exercise. Start out by doing them three times per week. Don't worry if you perform less than the recommended number of sets. Your strength will increase.
Push-ups are an all-time favorite of fitness buffs. This is because they build strength directly in the chest, arms and shoulders. Kneel down, place your hands about shoulder-width on the floor and extend both feet back. Inhale, and slowly lower your chest to the floor. Push your body up to a near full extension, then repeat. Once you have been doing these awhile, try to elevate your feet on a bed. This will hit the upper chest more directly. Performing them between two chairs, with both feet on the floor, will hit the lower chest.
Pull-ups work the lats or muscle. Adjust your chin-up bar in a doorway. Make sure it is secure. Allow enough room for your head when you pull yourself up. You will need to bend your knees. Grab the bar with both hands, take a deep breath, exhale, and pull yourself up. You may try doing these with your feet against a chair if they are too difficult for you. The chair can be used for leverage until your strength increases.
Lower the chin-up bar to waist level. Grab the bar with both hands and get underneath the bar at an angle. Take a deep breath, then exhale as you pull yourself up. Inhale as you go down. This exercise hits the major muscles in the back.
Kneel on a soft surface. Place your hands in front of you. Lift one leg up and extend it backward. Repeat with the other leg. This exercise will strengthen your lower back.
If you have expander cables, do some lateral raises for shoulders. Make sure you hit the front, side and rear shoulder muscles. Just step on the bottom part of the cable. Lift up in front of you and to the side to hit the front and side of the shoulder. Bend over or lean forward with the cable under your legs to work the rear deltoids.
Free-hand bicep curls can be done anywhere. Lock hands and pull one arm toward your shoulder, keeping constant resistance with the other arm. Repeat with the other arm.
Grab a towel or rope. Place your hands about 4 to 6 inches apart and do one-arm curls. This hits the outside area of the bicep more.
Take the towel or rope above your head, still maintaining the above grip. Bend one arm at a right angle behind your neck. Applying constant resistance to one end, pull the towel up until the arm is fully extended, then lower it back down. Repeat with the other arm. This exercise works the triceps.
Lean against the chin-up bar, which should still be at waist level. Use your triceps and dip down underneath the bar, then push yourself up. You may need to vary the angle depending on the degree of difficulty.
Triceps presses on a bathtub, hearth or slightly elevated platform work the lower area of the triceps. Sit on the tub ledge or platform. Place your hands down on top of the tub and lower your weight to the floor. Push yourself back up, then repeat.
Hand grippers can be used to add forearm strength. Use can also squeeze a tennis ball.
Do sit-ups, crunches or leg lifts to build strength in the abdomen area.
Squats are a great way to build leg strength. Place your hands behind your head, bend your knees until the legs are parallel with the floor, then push yourself up. An alternate exercise is to do deep knee bends, though a full-squat motion can be hard on the knees.
Lunges provide cardiovascular benefits and work the legs, buttocks and lower back muscles. Place your hands at your waist and step forward with one leg. Repeat with the other leg.
Calf raises should be done on the steps to get a better stretch. Start with 10 repetitions and build up to as many as you can. The calf is a stubborn muscle and needs a lot of stimulation to grow and get stronger. Later, try doing them on one leg, then alternating positions.