To build bigger arms and get stronger on major exercises such as the bench press and military press you need to follow a tricep exercise routine. The triceps muscles on the back of the upper arms make up most of the arms muscle size and assist on most shoulder and chest exercises. Whether you're into powerlifting, bodybuilding, or just weight train as a hobby you need to perform tricep exercises regularly.
One popular triceps exercise is the close grip bench press. It's basically done the same way as a normal bench press but with your hands gripping the bar close to the middle of it only 6 or so inches apart. This puts more of the focus on the triceps rather than the chest, though you may still feel it in the outsides of your pecs. When you do close grip benches you may be better not lowering the weight all the way to your chest because you may be putting too much stress on your wrists if you do.
A great alternative triceps exercise to the close grip bench press is the reverse grip bench press. You do them by using a normal or wider grip on the bar with your hands in an underhand position like on bicep curls. Reverse grip benches don't seem to put as much stress on the wrists and you won't feel them in your pecs as much as with close grip benches. Reverse-grip bench presses do take some getting used to so you should make sure ot to go very heavy when you first try them.
Triceps extensions are another great trcep exercise that can be done many different ways. They involve holding a weight overhead with you arms straight, then lowering it behind your head and raising it using your triceps when you do them standing or seated or holding a weight over your chest with the arms straight and lowering it to the top of your head when you do them lying. Standing and seated tricep extensions can be done with a barbell, EZ curl bar, dumbbell, or cables. You'll want to keep your upper arms as straight as possible while you do standing or seated triceps extensions and you must be careful not to cheat too much or use so much weight that you put too much stress on your elbows. Nothing will make your elbows sore quicker than cheating on tricep extensions with a ton of weight and overstretching the tricep attachments.
Lying tricep extensions are also known as skull crushers and probably won't put as much stress on your elbows as the standing and seated varieties since you'll have to stop the weight before it hits your head. One great high intensity technique is to do lying tricep extensions to failure and burn out by immediately performing a set of close grip benches with the same weight.
Cable pushdowns done with a bar or rope are excellent triceps exercises to do towards the end of your workout. These exercises allow you to get a strong contraction in the triceps at the end of a rep. You can pull your hands outward when doing rope pushdowns to really get a great tricep pump. Whether you're doing cable pushdowns with a bar or rope you can actually use your abdominal muscles to help get some extra reps after you've done as many as possible with good form.
One great isolation tricep exercise is the kickback. To do them hold a light dumbbell in one hand, bend over a bit, keep your upper arm at your side parellal to the floor and your forearm facing down, raise your forearm until the arm is straight to get a strong contraction in the triceps.
One you take advantage of the right tricep exercises you'll be on your way to larger arms and more overall strength.