How do polar coordinate systems work?

A polar coordinate system is just another method to determine a position of a point in space just like the cartesian coordiante system does; which hopefully you are confident with now. At A-level all you need to understand is how to apply this new system in 2 dimensional space. 
Unlike the cartesian system which uses parameters (x,y) the polar system uses (r,θ) where r≥0. r is the radial distance to your desired point ("as the crow flies if you will") and θ is the angle in radians from the x-axis on the origin which gives the direction in which the point is located. This would mean if θ = 0 the point you were describing would have tolie on the positive x-axis. If r = 5 then the point would be in cartesian form (5,0). As you can see this method allows you to describe all points on a graph and can be useful to depict graphs that would otherwise be very complicated in the cartesian system such as r = 3+2cos(θ) which forms a horizontal heart shape.