The push-up is a great exercise for strengthening the core and upper body. It can be done anywhere!
Start in the plank position
Toes on the ground and hands about shoulder-width apart
As you go down towards the ground, try and bring yourself forward so that your elbows go back as opposed to out
Keep your entire body tight and fluid
Try and keep your body rigid throughout so that your upper body isn't raised above your legs in a noncongruent fashion
You can also use a bench to decrease the intensity and focus on form