In order to understand projectile motion you have to look at the motion in two planes - the horizontal and the vertical.

Horizontally

The projectile is moving with no force acting on it (except air resistance which you are able to ignore in most cases. There is there force no acceleration (F=ma) so the projectile moves at a constant horizontal velocity all of the time it is in the air.

velocity_{H} = displacement_{H} / time taken

Vertically

The projectile is moving under gravity. It is therefore suffering a force making it decelerate as it rises and a force making it accelerate as it falls. The acceleration due to gravity is 9.81 ms^{-2}.

You can use Newton's equations of motion to calculate the time the projectile will be in the air or the height it rises to. (You can use them because it is a situation where a constant force is acting).

You can use them because its vertical movement is a situation where a constant force is acting – and that is the case if it moves under gravity with no other forces of significant size.

v _{V} =u _{V} + a_{V}t

Once you know how long the projectile is in the air you can work out the range of the projectile using velocity = displacement/time.