The triceps are a fairly easy muscle group to train. Their job is simply to extend the arm. Your job--as a bodybuilder--is to hammer the living daylights out of them every time you train them. Here's how.
If you do triceps after chest or shoulders, they should be pretty warmed up before you even get to your first isolation exercise. Even so, you should do on warm up set and stretch them out some before going heavy. If your triceps are lagging or you're hitting them first in your workout for some other reason, be sure to do at least two warm up sets and some light stretching before you dive into the work sets.
Once you're ready to go, I wouldn't recommend doing more than three exercises. It's really only an opinion, but volume training approaches don't tend to pay off as well as heavy duty-esque routines unless you happen to be Arnold Schwarzenegger or a direct descendant.
I always flex and hold my tricep movements for a split second before I go into the negative portion of the rep. I'm happier getting six reps with this kind of form than whipping through eight or nine slopper reps. Don't get caught up in the numbers game because you'll lose. Build your muscles not your ego.
On to the exercises...
Stand facing a pulley that's set to a height slightly above your shoulders. You can perform this movment with a variety of grips. The most popular ones are the straight bar, the triangular pushdown piece and the rope. To start the movement, grap hold of your grip of choice and fully extend your arms downward. If you're using the rope hammer grip, then push your hands apart at the bottom of the movement to get the full benefit of that specialized grip.
Your feet should be less than a foot back from the pulley to provide maximum leverage and stability. I always put one foot forward and lean into a little bit over the weight.
If your arms are unevenly developed then I strongly recommend isolating each arm in turn starting with the weak one by using a one-hand grip. You can opt to do the pushdowns with either a palms-up or palms-down grip, but I find it easiest to work with the one-hand grip if I use a palms-up grip. This tends to work the posterior head of the tricep a bit more, but the anterior head sees so much action during chest and shoulder movements that it doesn't really need more than five or six work sets to itself.
Triceps.
There are two heads to the tricep muscles, both of which need to be worked to achieve maximum overall development. The rope hammer grip will help you hit the posterior head as will using a reverse (palms-up) grip on the straight bar pushdowns.
With a single light dumbbell, stand to one side of a flat bench. If you are working your right arm then you would stand to the left of the bench, put your left knee and left hand on the bench for balance and lean over so that your back is running above the bench parallel to the floor.
Raise your right elbow to your hip and let your forearm and hand dangle straight down. Keeping your upper arm at your side, extend your arm so that it is completely straight. Lower slowly.
To work the left arm just swap everything to the other side.
Triceps.
This is a great peak contraction movement and it will help build mass along the lower part of your arm because of the attention it gives to the anterior head.
Use a moderate weight on an E-Z curl bar and lie on a flat bench. Start with your arms fully extended. Keeping your elbows pointed forward, lower the weight to your forhead--or if you prefer--justbehind your head. Use your triceps to extend your arms and bring the weight back up to the original position. The bar should travel in a smooth arc at a regular speed. In other words, don't hyperextend your lats and then use them to whip the bar back up.
Triceps.
This has--and always will be--a personal favourite of mine. You should consider doing something that works both arms independently if you have a strength imbalance because this movement will tend to worsen the problem.
You can use either an EZ Curl bar or a regular barbell for this movement. It is performed lying down on a bench in the same manner you'd perform bench press. The difference is that your hand positioning is much closer together. I usually space them so that I can almost touch my thumbs together if I were to extend them. If this close grip gives you trouble keeping the bar balanced then use the shorter and easier to control EZ Curl bar.
Lower the weight down to your chest and power it back up. I prefer to do keep my arms slightly bent at the top of the movement and refrain from locking my elbows. I feel that locking your elbows takes the stress off your triceps which is not the goal at all.
Triceps, inner pectorals to a certain extent.
This is especially hard to do after a chest workout, but if you work triceps with some other muscle group then this is a good movement.
Sit down on a bench with a back rest and maneuver a moderately heavy dumbbell behind your head so that your holding it with both hands. Point your elbows forward and extend your arms raising the weight above your body. Lower the weight down as far as you can before raising it back up. If you find that you simply can't raise it once you've lowered it past a certain point then you need to choose a lower weight.
Triceps, minor secondary stress on front delts.
The hardest thing about tthis movement is keeping your elbows from pointing straight out.