Gym machines are good for isolating specific muscles, but since they force the body into a set movement pattern, they often lead to injuries. Dumbbells will allow you to go through a greater range of your natural motion, and will recruit more stabilizing muscles. While lifting, mentally focus on stabilizing your core and contracting the targeted muscles.
Goblet squats: cup a fairly heavy dumbbell vertically in front of your chin with both hands. Keep it out as far away from your face and squat down. Focus on sitting down between your heels and make sure your knees don’t extend over your toes. To come up, focus on pushing the ground away from your feet.
Dumbbell side bends: plant your feet shoulder width apart and bend your knees slightly. Keeping your hips square, lean over to one side from your waist, holding a fairly heavy dumbell in the hand of the side you’re leaning to. Lower slowly to the side, and then quickly return to stand. Do fifteen reps on each side.
Push-ups: focus on keeping your back flat, your abs in, and lower your chest all the way down to the floor. A key to push-ups is to focus on pushing the ground away from you, rather than on pushing your body back up. Do as many as you can, and then do a couple more. There are number of variations of push-ups which will help you hit different muscles. Super wide-grip push ups will work your upper back, biceps, and delts. Chataranga push-ups (elbows in to your sides) will hit your triceps. Diamond push-ups (hands make a diamond right below your face) will work your upper back and traps more.
Back-extensions: these are amazing for strengthening the oft-neglected back muscles and strengthen your hamstrings as well. Lower your body on the Roman Horse and lift up slowly–you should feel this in the back. Thinking about your hips as a fulcrum, lower slowly and come back up quickly. You can experiment by twisting your body to the side to hit different back and side muscles.
Bicep curls: stand with your feet shoulder width apart and let a pair of dumbbells hang at your side. Don’t let your arms come forward by focusing on keeping your elbows near your waist and try to focus on lifting with your biceps and not your shoulders.
Tricep dips: place your arms behind you on a weight bench right underneath your shoulders with your feet shoulder width apart a couple feet in front of the bench. Keep your knees bent and focus on lowering your butt to the ground and lifting back up with your triceps alone.
Hanging leg raises (level of difficulty: 1000): hang from a pull-up bar. If this is hard, you should work on it, trying to increase the time you can hang each time you’re in the gym. Once you can hang comfortably for thirty seconds, begin lifting your knees slowly into your chest–don’t swing! If this is difficult, you can also use the Captains Chair and do slow leg raises. Do as many as you can with straight legs, bent knees, and on each side to hit different muscles.
Pull-ups: once you’re comfortable hanging from the pull-up bar, the pull-up is, by far, the single most effective exercise for increasing strength. Chin-ups (hands facing in) are easier as they recruit the biceps more so than regular pull-ups do. Work on these, and then start doing baseball grip pull-ups (one hand in, one hand out). Once you can do five of these on each side, start doing regular pull-ups. You can experiment with grip-width to strengthen all different muscles in your back. While pull-ups can definitely help tone, they will probably add muscle mass to your back, as they work muscles you don’t normally use.