Push-Ups are a great exercise for the core and stabilising muscles, as well as for the chest, shoulders and arms.
Push-Ups are an excellent upper-body exercise to build strength, muscular endurance and power; perfect for muscle isolation whilst tying in the core and working the chest and arms.
1. Position your hands on the floor slightly wider than shoulder width apart. Rotate the arms so the crease in the elbow is facing forward. This will help lock the shoulder in. Keep your legs together and make sure you core, abs and glutes are under tension. (See Fig. 1)
2. Keeping your torso straight lower yourself towards the floor, bending at the elbows and feeling the tension across the chest. Your upper arms should be tucked close into your torso as you hit the lowest point. (See Fig. 2)
3. Engage the chest and triceps and push back up, straightening the arms back out.  Maintain a neutral spine throughout. Repeat the movement from point 2.

Fig. 1

Fig. 2

Throughout the whole movement the body should be tense, with your abdominals drawn in and shoulders positioned back and down.