How do I find a stationary point? And how do I determine whether it is a maximum or minimum point?

In order to find the stationary points of any funcion, you must differentiate. Once you have differentiated, the deriviate of this function must be set equal to 0, in order to determine what the stationary points actually are.

Once you have found the stationary points, in order to determine their nature, you must differentiate the function again. Finding the second derivative will allow you to see whether the stationary point is a maximum or minimum, by substituting in the coordinates of the stationary point. If the value turns out to be positive, then the point is a minimum. However if the value is negative, then the stationary point is a maximum.