One of the best ways to increase your bench press and reduce risk of injury from benching is to improve your bench press stability through some mental cues. Keeping your entire body stable seems simple with light weights, but once you are near your maximum bench press weight then you start to notice minor shifts that can throw off the whole lift. Here are some cues I try to remember during my bench press sets:
Keeping your upper back tight and contracted during the entire bench press motion is challenging, but can lead to the best results. I typically try to do this by getting into place on the bench, then lifting my whole upper body off the bench by using the bar above me in the rack. Before putting my body back down on the bench, I pinch my shoulderblades together and try to push them down towards my legs. Then, once together, I pin my shoulderblades to the bench and really force my upper body against the bench. This helps to keep my shoulders in a better position and gives my chest and arms something to push back against during the lift.
The biggest sign of an unstable bench press position is when your legs are able to move during the lift. Even though the bench press is mostly a chest and triceps movement, using your entire body to brace will help you squeeze out the most force against the bar. I usually get my feet in place by placing my heels just under my butt, then pushing on the floor hard enough that my butt is almost (but not quite) lifted off the bench. By pushing down like this right before lifting the bar off the hooks, my legs are engaged and I've got another point of contact with a solid point.
Once my shoulderblades and feet are in place, but just before unracking the bar, I take as big of a breath as I can down into my belly. This pushes out against my abs and obliques to form a strong core. I try to hold this breath throughout the entire lift if possible (without passing out), but if the set is more than about three reps then I'll usually have to pause before the fourth rep to get another big breath. This same bracing of the core is important for all compound lifts, but I find that most people leave it out for bench press the most. Bracing the core, with a pinned upper back and engaged legs, will make the most stable position for you to maximize your bench press and hit new PRs!