The Major Muscles used in the Bench Press Exercise are the Pectoralis Major, Anterior Deltoid, Coracobrachialis and the Triceps.

With feet on floor or bench, your spine, pelvis and wrists in neutral, the upper arms angled at 80-90° from torso and forearms perpendicular to floor, contract abdominals and lower weight with control.  Press up extending without hyperextending. Exhale on the upward phase.  Inhale on the downward phase.

Lie supine with feet flat on floor (or on bench or boxes if you have low back issues).
Spine and pelvis are in neutral (natural position). If you have low back issues then press lumbar spine
flat with pelvis posteriorly tilted (bring forwards a little bit).
A wide, closed pronated grip is typically used but if you want greater Triceps involvement use a narrow grip
with hands evenly spaced.
Upper arm is angled at 80-90 degrees from torso and forearms are perpendicular to the floor. Wrists
are as neutral as possible.
(see picture
above).  If you are experiencing shoulder pain, shorten your range of motion.  In the down phase, bring elbows in towards ribs.

In an upward starting position, contract abdominals and lower weight with control. The only joints
moving are shoulders and elbows, all other joints remain stabilized.  Barbell should be in the mid-chest (nipple) area.
Press up, fully extending and taking care not to hyperextend (lock) the elbows.
Exhale on the way down.  Inhale on the way up.

Common errors: 
– Shoulder joints roll forward when elbows lowers
– Uncontrolled descent
–  Extreme end range of motion (elbows go too far down)
putting stress on the shoulder joint
– Wrist rolling
– Back arching
– Hips pressing up
– Bouncing bar off of chest
– Hyperextending elbows
– Holding breath
– Lifting too much weight so as not to be able to 
maintain proper form

Opposing Exercise: Upper back exercises such as the Reverse Fly, Horizontal High Row and one of my favorites Cable Face Pull with External Rotation.