How to Perform Triceps Dips
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 triceps dip is a compound push exercise targeting the triceps brachii, comprised of the long, lateral, and medial heads. The anterior or front deltoid, sternal and clavicular heads of the pectoralis major, pectoralis minor, rhomboids (middle back), levator scapulae (rear neck), and latissimus dorsi are supporting muscle groups during this movement. 
Supporting muscle groups assist the target muscle group(s) during the movement. The biceps brachii (short and long heads) and lower trapezius act as stabilizers during this exercise.  Stabilizer muscles help maintain a posture or fixate a joint by contracting without significantly moving. 
The triceps dip is consistently ranked one of, if not the best compound movement for adding tricep size and strength. The primary difference between triceps dips and chest dips are the angle of your torso and forearms throughout the movement.
How to Perform the Triceps DipDetermine whether you're going to perform this exercise with assistance, bodyweight-only, or with added resistance.
Popular triceps dip assistance options include a dip machine with a counterweight platform, exercise bands wrapped around each bar and the upper shins, as well as a training partner holding your shins and supporting you through sticking points. Popular triceps dip added resistance options include a dip belt holding a weight plate, crossing the shins to hold a dumbbell, wearing a weight vest, or wrapping chains around the upper body.
Once you've selected your desired resistance approach the dip bars, they may be two free-standing metal bars, an add-on attached to a cable tower, or part of a standalone machine. The dip handles may run parallel to each other or made a V-shape.
Grasp the bars with a shoulder-width neutral or hammer grip (palms facing each other). Avoid taking a grip wider grip as this will increase chest muscle fiber recruitment and take stress off of the triceps. Avoid taking an excessively narrow grip as this may cause excessive internal rotation of the shoulder leading to discomfort and impingement.
You can take a traditional grip (thumbs wrapped over the fingers) or a false grip (thumbs and fingers on the same side of the dip bars). Experiment with various grip type and width combinations to see what feels most comfortable and natural to you.
Now that you've set your grip type and width set up on the dip bar so that your arms and elbows are straight (but not hyperextended) and your shoulders are in-line with your hands. Your torso should be upright with no bend in the hips. You can keep your knees straight (but not hyperextended) or bent at a 90o angle throughout the movement. This will be your starting position. If the dip bars are high off the ground use a step or quickly hop up to this top position.
After setting your starting position take a deep breath, brace your abdominals for impact, squeeze your glutes, and begin lowering your shoulders towards the dip bars. Initiate this lowering by bending the arms and allowing the elbows to drift in-line with and behind your hands. Your forearms should break perpendicular with the ground. Unlike chest dips you should try to stay as upright as possible throughout the entire movement.
Continue bending the elbow and upper arm until you feel a nice stretch in the shoulders. Depending on shoulder flexibility this depth will be at or lower than when your shoulders are in-line with your elbows. Hold this bottom, stretched position for 1 to 5 seconds.
Initiate the return to the starting position by flexing the triceps and pushing through the palms. Continuing pushing the body upwards until the reach the original start position. Complete for the desired number of repetitions.
Some lifters choose to exhale while pushing up from the dip bars or in between in each repetition. Choose a breathing pattern that feels the most natural and comfortable for you. If something feels off your shoulders, triceps, or chest, then terminate the set immediately. This exercise can cause significant discomfort in those with shoulder flexibility issues.
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.
Tricep Dips Form TipsAdd Weight - If you can successfully complete sets of 15+ reps with bodyweight then consider adding weight. Increasing resistance is an excellent variable to adjust for continued progression and muscular overload.
Popular triceps dip added resistance options include a dip belt holding a weight plate, crossing the shins to hold a dumbbell, wearing a weight vest, or wrapping chains around the upper body.
Perform Negative Reps - If you cannot perform full range-of-motion bodyweight triceps dips and don't have any assistance implements then perform negative reps. To perform a negative you simply start at the top of the exercise and terminate the rep at the bottom, stretched position without pushing your body back up to the start position.
Negative reps are an excellent tool to overload the tricep musculature and are the stepping stone to full range-of-motion triceps dips.
Use Assistance - If you cannot perform full range-of-motion bodyweight triceps dips and do not feel comfortable performing negative reps then use assistance implements. Popular triceps dip assistance options include a dip machine with a counterweight platform, exercise bands wrapped around each bar and the upper shins, as well as a training partner holding your shins and supporting you through sticking points.
Watch the Shoulders - Throughout the entire triceps dip repetition ensure your shoulder blades remain retracted and secured. If you find yourself rolling your shoulders excessively rolling forward or drifting up towards your ears then terminate the set and potentially decrease the resistance.
Drifting shoulders can increase injury risk and decrease engagement of the target muscle group.
Hold the Stretch - If you're looking to increase intensity then experiment with holding the bottom, stretched position of the triceps dip for 5 to 10 seconds. Really focus on squeezing the pectoral muscles. 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.
References1) "Triceps Dip." ExRx (Exercise Prescription) on the Internet. N.p., n.d. Web. 4 Nov. 2015.
2) "Kinesiology Glossary." ExRx (Exercise Prescription) on the Internet. N.p., n.d. Web. 4 Nov. 2015.