The Floor Press is a great progression for people that can do push-ups and that are looking to move up a level. This exercise is a good stepping stone between push-ups and bench pressing.
By lying on the floor you take out any lower body involvement meaning that you have more focus on your chest muscles. Also this creates a limitation in how low you can go with your elbows, which causes less stress on your shoulders. So this can be a good alternative for people that still want to press heavy but have shoulder issues.
To set-up start with the dumbbells on your thighs and use your legs to nudge them into position. Legs can be straight out or bent. Arch your back as you would with a normal bench press and choose your elbows position, either 45 degrees or tucked in. This can also be done the same way but single-arm with your off arm to the side for balance (remember to brace your core).
Once the dumbbells start to get too heavy to lift into place by yourself you may need someone to lift them into place for you or move onto doing a Barbell Floor Press where it is easier to set-up by yourself and lift heavier.