Everyone is looking for ways to increase their bench press and pressing power, and it is normally the hardest thing to increase even though there are many different exercises out there for this.
Most people can do with stronger triceps and there are lots of triceps heavy exercises and isolation exercises that can be done, some which work and some don't.
One exercise that I have found to pack on triceps size and power, and has a good carry over to benching and all pressing in general is the close grip floor press (CGFP).
The CGFP is a relatively easy movement to do and is safer than benching if you have no spotters or power rack, because unless you are pretty big you can drop the bar onto the floor and will be able to get out from under it.
You technically don't need a rack at all, but trying to get the bar straight off the floor can be hard and I don't recommend it. The best setup is either a power rack or squat rack in which you can lay down in, where your eye level is looking up at the bar. The bar wants to be high enough so you don't need to unrack it far, but you want to make sure you can unrack and rerack with enough clearance from the pins.
You may have heard of floor press, but the people I see performing it do so incorrectly in my opinion do not get full effect and benefits. I recommend your legs to be completely flat on the floor, this takes any leg drive out of the movement and makes it a pure pressing power move. Do not arch your back as there is no need to decrease the rom (range of motion). Make sure to use a close grip, which for me is so my index finger starts on the knurling. If you do it in this way it should be very similar rom to your full bench when you have an arch and a wider grip.
Push your lats and shoulder blades into the floor before you unrack the bar and proceed to unrack the bar, keeping it at lockout till you feel stable enough, then start descending the bar, make sure that this descent is under control, so when your arms touch the floor you don't lose tightness or cause a shock to move the bar out of the line. I believe the best way to increase effectiveness of the CGFP is to pause the rep when your arms are at the floor, this is because it takes out the flex action in your muscles. The pause does not have to be long, but you want to do it long enough so that you lose any flex energy and so you don't end up bouncing off the floor. Make sure that you keep everything tight while your paused.
When your ready to press make sure to press as fast as you can out the bottom, as most of the power will be coming from your triceps. You may find they tire out quite quickly. Proceed to repeat for X number of reps.
The floor press should be used as a replacement for your heavy bench for at least 4 weeks. I normally do sets of 3. I would not recommend any reps above 5 especially if you plan on doing any other triceps movements in that session.
If your weakness is off the chest in the bench press it may not help much, but if the weakness is when your triceps start kicking in then close grip floor press should help increase your bench, especially if your an equip lifter. Not only like this but it will add good size on your triceps.
Try out the close grip floor press and comment what you think to it and how it goes for you.