How to Perform the Overhead Dumbbell Extension
The triceps brachii is comprised of three muscle heads - the long, lateral, and medial heads. When these three heads are evenly developed they create the appearance of a horseshoe or upside-down U when flexed.
Bodybuilders looking to naturally increase their arm size as rapidly as possible should focus on compound and isolation movements targeting the triceps, rather than the biceps. Powerlifters who grind through the midpoint of or fail to lockout their bench press reps should hammer their triceps with compound movements.
The triceps are primarily built through pushing movements such as presses and extensions. These movements may be performed in a vertical or horizontal plane. Every balanced physique needs a beastly set of triceps.
The dumbbell overhead triceps extension is an isolation push exercise targeting the triceps brachii, comprised of the long, lateral, and medial heads. There are no supporting muscles groups to assist the target muscle group during this movement. However the anterior or front deltoid, clavicular head of the pectoralis major, and wrist flexors act as stabilizers during this exercise. 
Stabilizer muscles help maintain a posture or fixate a joint by contracting without significantly moving.  Although this movement engages all three heads of the tricep many trainees use this exercise to build the lateral head or outer tricep.
Those will preexisting shoulder conditions should approach this exercise with caution as it may exacerbate underlying issues.
How to Perform the Dumbbell Overhead Triceps ExtensionApproach the dumbbell rack and select the appropriate working weight. You will only need one dumbbell as this is a single dumbbell exercise. If this is your first time performing the exercise then pick a conservative weight that you can safely lift for 8 to 12 repetitions.
When in doubt, start with a conservative weight and work your way up; this will leave more room for progression and ensure you develop properly form early on. While this exercise can be performed standing most trainees find they can isolate the target muscle the best when it's performed seated.
Once you've selected the appropriate working weight grasp the dumbbell and place it near a flat bench or a seat with low back support. Adjusting a traditional bench so that it's completely upright will likely interfere with the range of motion for this exercise.
Sit on the edge of the bench so that your glutes are securely resting on the padding and your shins are perpendicular with the ground. Pick up the dumbbell and grasp it securely. The most secure way to hold a dumbbell during this exercise is to flip the dumbbell vertically and place both hands together so that your knuckles are facing you and you're supporting the inner portion of higher end of the dumbbell.
The fingers of one hand may be slightly resting over the fingers of the other hand. For those familiar with pop culture this grip may be referred to as the Illuminati hand sign which is also commonly used by the hip-hop rapper Jay-Z.
After securely grasping the dumbbell straighten (but do not hyperextend) your arms and elbows so that the dumbbell is directly over your head and in-line with your ears and shoulders. Your torso should be upright with a high chest and shoulders down and away from your ears. This will be your starting position.
Take a deep breath, brace your abdominals for impact and begin lowering the dumbbell behind your head. Initiate this lowering by bending your elbows so that your forearms move downwards while keeping your upper arm as vertical as possible. Ensure your wrists stay rigid so that you don't allow the dumbbell to sway and potentially hit your head.
Continue lowering the dumbbell until you feel a nice stretch in the triceps. For most this will be when the forearms are at a 45-60o angle with the ground. Hold this bottom, stretched position for 1 to 5 seconds. Initiate the return to the starting position by flexing the triceps and pushing the dumbbell upwards so that it's vertically in-line with your ears and shoulders. Complete for the desired number of repetitions.
The movement path for lower and raising the weight should be the same. Your upper arm and elbows should remain in a fixed position throughout the entire movement. If you find your elbows excessively bowing outwards or upper arms significantly moving then the weight it too heavy.
Some lifters choose to exhale while pulling the dumbbell from the bottom position or in between in each repetition. Choose a breathing pattern that feels the most natural and comfortable for you.
This exercise can be performed using straight sets, pre-exhaust sets, drop sets, rest-pause sets, supersets, trisets, giant sets, paused reps, partial reps, forced reps, or slow negatives. As with any exercise, the two most important components are high-quality form and progression. Progression can take a variety of forms (e.g. more weight, sets, or reps, decreased rest period, improved rep quality, etc...) but strive to improve every training session.
Overhead Dumbbell Extension Form TipsHold the Stretch - If you're looking to increase intensity then experiment with holding the bottom, stretched position of the overhead dumbbell triceps extension for 5 to 10 seconds. Really focus on squeezing the triceps and not relaxing in the bottom position.
This will increase time under tension and the burn in the triceps. Increased time under tension is an excellent variable to adjust for progressive overload and enhanced muscle growth.
Avoid Momentum - The overhead dumbbell triceps extension provides maximum benefits when it's perform in a controlled full-range of motion. Check your ego at the door and don't immediately attempt the 100lb dumbbell.
In addition to staying tight (glutes flexed, torso upright, chest high, and shoulders down) do not use momentum to bounce the dumbbell from the bottom position to the starting position. This momentum dramatically increases the likelihood of injury and minimizes the stimulus of the target muscles.
References1) "Dumbbell Triceps Extension." ExRx (Exercise Prescription) on the Internet. N.p., n.d. Web. 5 Nov. 2015.
2) "Kinesiology Glossary." ExRx (Exercise Prescription) on the Internet. N.p., n.d. Web. 5 Nov. 2015.