Here are some of my favorite triceps exercises in order:
1. Close-grip triceps press- This is the king of the triceps exercises in my opinion because you can load the triceps with the most weight therefore hitting more muscle fibers. The key is to make sure that you keep your elbows tight to your sides while lowering and pressing up with the bar. Make sure to focus on the drive coming from your triceps. I would use anywhere from a 6-10 inch wide grip on the bar depending on what you like best. If you go too narrow you might find it hurts your wrists.
2. Dips- Another classic that not many people think of being the "one of the best." Make sure you go all the way down until your biceps touch your forearms. If you need to add weight use a weighted belt. Try and focus on keeping your body position straight ahead and don't lean down since this will shift more focus on the chest.
3) Decline close-grip presses- These are done just like the regular close-grip presses except they are on a decline bench. Decline presses have been shown to hit up to 10% more muscle fibers....this is good!
4) Seated upright rope triceps extensions- Sit on a upright bench that has a back support. Put the cable pulley machine down low and attach a rope. Have someone hand you the rope and extend it up over head and then twist at the top before lowering. This really hits the inner tricep known as the long head. Most guys don't get work to this area so you should try this!
5) Decline dumbbell triceps extensions- You will get a great stretch of the triceps. Lie on a decline bench and grab dumbbells with your palms facing each other. Keeping your upper arm still, lower your forearms until they hit your biceps and then drive them up.