Big triceps, genetics aside, aren’t really that difficult to get. The following is how you can acquire them, relatively easily.
Press Exercises
Push movements should consist of the primary exercise in your tricep workout regimen. The reason is that they incorporate the entire muscle group (i.e., all three heads, meaning the long, lateral, and medial heads) and, therefore, require more energy overall; in other words, difficult exercises should be (and are traditionally) performed first. Consequently, they also provide a natural warm-up for more concentrated (not to be confused with concentration) exercises. Among the most common are close-grip (flat) barbell bench press and dips (performed either with your hands placed at the side-edge of a bench… or completely suspended [for increased difficulty]).
Something else worth mentioning is that consistently training your chest (and, to a degree, your shoulders) properly (i.e., using proper form) naturally helps in this area, too. Why? Because, as you might have guessed, the pressing movements are staples with those particular muscle groups. And while they might not be focused on the triceps, they tend to enhance this part of the body as well.
Number of Exercises and Sets
The number of exercises performed for the triceps should exceed that of the biceps. Let me elaborate. Many have argued that bodybuilding is an illusion; this includes the opinion of several winners of major competitions. And since the triceps consist of approximately two-thirds of the size of your upper arm, you should train them more than the biceps (without altering the workout schedule frequency [i.e., number of times per week that you work them out]). This doesn’t need to be accomplished exclusively by means of increasing the number of exercises; however, a balance between that and a higher number of sets is recommended.
As a side note, the number of repetitions per set is generally not recommended to change, either (because this is typically done to shift its intended purpose [e.g., higher reps are usually reserved for fat-burning, while a lower number of repetitions strongly contributes to muscular development]).
Full Extensions
Full extensions (allowing for a full range of motion in the contraction phase) may assist and play a role in the hypertrophy of your triceps. The eccentric part (lengthening/stretching the muscle group) is obviously of great importance, but so is the concentric portion, especially when leading to a fully contracted tricep. The latter is where many lifters lack when working out the triceps brachii, at least where maximizing your gains is concerned.
Rest Following Your Workouts
We can’t stress this enough. It’s important to rest after each training session for optimal results in both the long and short term. You will, quite literally, see your triceps getting bigger on an almost weekly basis if every tricep workout is followed by a nap or relaxation period (with a light, protein-rich meal or shake in between, of course). This may be general advice, but it’s still a very necessary (and often overlooked) contributing factor.