How does circular motion work?

Firstly, let's remember Newton's laws which tell us that in order for something to change direction of motion - like: going around in a circle - a net force needs to be acting on the object. In the case of circular motion, this force is "pulling" the object, e.g. a ball on a string or a car on the road, towards the centre of circle. This causes an acceleration (because F=ma), and so the object is diverted from a straight path along the tangent of the circle, making it curve around the bend. If you will, the object is continuously trying to remain in a straight path, but the force keeps pulling it inwards. This is also why it often feels as though, when you're going around a bend or stand in one of those fairground rides, it feels as though you are being pushed outwards, even though the force is acting towards the centre of the circle. That's because at each instant you - the object in this example - want to continue travelling in a straight path along the tangent of the circle, but the force (e.g. your car seat or the wall of the fairground ride) push you inwards, making it seem like there is a force pushing you to the outside of the circle.