In order to try and help you understand perspective a bit more, I have made the two animated images below. You will see the first one start with the horizon line, then the vanishing point will appear. Next the orthogonals will be drawn in. This is exactly what artists do when they prepare to paint on a canvas or some other surface. Then the front of a building will be drawn in. From the upper corner of the building another orthogonal is drawn and then the back side of the building. 

At this point, the painter starts to cover over the orthogonals and horizon lines by filling in the objects, so you will see the front of the building filled in and then the side. If this process were continued, all of the lines would be hidden and just the scene would remain.

The second animated image shows you how to find the vanishing point. Take any straight lines presented to you in the painting (in this case, our building) and, by using a ruler or piece of paper, follow along them to where they meet. There is the vanishing point. 

Some paintings are easier to do because they have at least some straight surfaces in them. Others have no straight surfaces, like outdoor scenes with no buildings. These are definitely harder to work with, but if you work at it, they can be found. 

Should I mention at this point that some pictures have two vanishing points? Or that the vanishing point can actually be off the canvas? Don't worry about that. There are plenty of pictures to choose from that have an easily discovered vanishing point. 

Remember--hit reload and then scroll down to the images below.