If you have access to dumbbell set, then you will be able to perform quite a few good dumbbell exercises for developing and toning the arm muscles. These exercises work best with an adjustable dumbbell set such as the Bowflex SelectTech 552 Dumbbell set where you have access to all the different weight increments. If you have just a few dumbbells at home, some of the exercises may have limited use if the weights you have are too heavy or too light for them.
Dumbbell Bicep Curls. This exercise would be the most important for overall development of your biceps. For more information on this exercise, read my article The Different Ways of Doing Dumbbell Bicep Curls.
Hammer Curls. This exercise is much like a Bicep Curl with one difference. Instead of curling the weight with your palm facing upward, it's facing inward as you lift the weight, much like how you would position your arm for using a hammer, thus the name. Doing the curls this way also develops the forearms.
Concentration Curls. Unlike the other bicep dumbbell exercises, this one is performed one arm at a time. Sit on a bench and rest the elbow of the arm you will be working out on your knee. Curl the weight up towards your chin, really focusing on the pump you get in your bicep. You generally use much less weight for Concentration Curls than other bicep exercises as the point of it is to do them slowly and controlled to feel the burn.
Dumbbell Triceps Extensions. Take a dumbbell and sit down on a bench. Put your arm behind the back of your head with your elbow bent and press the weight upward with your triceps with as little movement as possible in your upper arm. When you are done the set with one arm, switch to the other.
Lying Triceps Extensions. Lie down on the bench and have your arm to the side of your head with your elbow pointing upward. Press the weight upwards until your arm is almost straight up in the air and come back down. Once you are done with one arm, switch to the other. A variation of this movement is the Cross-Face Triceps Extension where instead of having your arm to the side of your head, your arm is rotated to the side so that your forearm is right in front of your forehead. You then press the weight up, with the ending position again being your arm nearly straight in the air.
Kickbacks. Bend forward or lean on a bench with the side you are not working out. You upper body should be parallel to the ground with your opposing foot on the floor. With your opposing arm take the weight and have your upper arm aligned with your body so that its also parallel to the ground but your forearm is angled so that it is perpendicular to it. Press the weight up using your tricep so that your entire arm is nearly straight. Kickbacks are generally used for toning with low weights and high reps. You cannot safely do heavy weights with kickbacks as that will put too much strain on your elbow and you'll risk injury.
Wrist Curls. Take you dumbbell in one hand and rest your arm down on your leg (or on the bench) with your wrist facing upwards and hanging off your leg past your knee. Extend your wrist as far down as possible and then curl the weight up without moving your forearm and repeat. Once you are finished your set, switch to the other arm.
Reverse Wrist Curls. This exercise is pretty much done in the same way as wrist curls with the exception that the palm is facing towards the ground instead of upwards. This is where having an adjustable dumbbell set comes in handy as you can make one side of the weight heavier than the other. You'll notice that reverse wrist curls become much more effective when the weight is unevenly balanced like that. I use the Bowflex SelectTech adjustable dumbbell set. You can read my review of it here.
Other dumbbell workouts you can do:
More of my workout advice:
Are Bowflex SelectTech Adjustable Dumbbells suitable for you?
Should you buy Bowflex SelectTech Dumbbells in a store or online?
Why you would want to use barbells for your workouts
Why you would want to use dumbbells for your workouts
How I lost over 40 pounds in 6 months with some simple diet changes
Upper body exercises with no equipment needed
Lower body exercises with no equipment needed
Cardio exercises with no equipment needed
The Different Ways of Doing Dumbbell Bicep Curls
Inflatable Exercise Ball Exercises for Men