These are the basic push ups that I do when I'm training triceps - usually at the end of my work out. I pick two of these variations and do 3 sets of each (reps depends on how strong I'm feeling).
01 Push ups (elbows back)
Have your hands shoulder width apart and pull your elbows back when you come down. Keeping your elbows tight to your body will target the triceps (elbows going onwards will hit chest).
02 Explosive push ups
These are the same as above, but explode up and take your hands off the floor. Once these become easy, lift your hands further off the ground (touch elbows or shoulders).
03 Forearm push ups
Start in a standard push up position, but lean forward on your feet. Once you're at the bottom of the push up, slide on to your forearms by lowering them to the ground and pivoting on your toes. Remember to come all the way down before you drop on to your forearms!
04 Diamond push ups
These are my favourite triceps exercise. Use a close grip, with your thumbs and index fingers touching (to make a diamond shape). If these feel too hard on your wrists, have your hands slightly further apart.
05 Reverse grip push up
These are a standard push up, with a reverse grip. Keep the movement as up-and-down as possible to avoid accidentally doing the much harder variation used for to target your shoulders.