"Skullcrushers" (also called a "French press") involves bending your elbows to hold a weight (like a dumbbell) at or near your forehead, then extending your elbow to press that weight to full extension away from you. This can be done lying down on a flat bench or at a slight incline. The barbell version can be used the same way or use an EZ bar.
There are three tricep muscles, Medial, lateral, and long heads. The medial/lateral are recruited only by movements at the elbow joint while the long head can be recruited by movements at both elbow and shoulder joints. If you look a anatomy picture of the upper arm muscle....you will see where these are. The skullcrusher hits the Long Head muscle which you use to raise your upper arms over your head. Tricep pushdowns and dips train the lateral and medial heads.
I do mine lying on a flat bench with my head close to the end so the dumbbell clears when lowering it. Then keep my elbows in and point above my head to keep tension on the triceps throughout the motion. I raise the dbl longways "I" to where it is above my forehead and then back down in a controlled motion. If using a barbell or EZ bar, Do Not flair out your elbows to the sides as this will harm the joints and puts more of your shoulder into the work.
Be sure you have a good grip when doing this AND if using adjustable bar/plates dbl, that the plates are tight. The last thing you want to do is have it slip and find out how the "skullcrusher" got its name
Overhead extensions is placing the upper half of your arm (if doing one dumbbell at a time) or arms (if using both with one dbl or two alternating or together) alongside your head about parallel to each other. Then pressing your elbow from a bent position to fully extended above. You can do this seated or standing.
Dips are really good tricep builders. Just make sure to keep yourself straight upward and do not lean. You can do this with dipbars or just with the bench.