Exposure is the result of the amount of light the film or camera sensor receives during a single shot. The consequence to the resulting picture is very important, too much exposure and your shot will be a white out, too little and it will be very dark.
How do you control the exposure? Easy! Use shutter speed, ISO and aperture and combinations thereof. How do you measure exposure? Easier! When you look though the view finder of any DSLR you will see a light meter at the bottom of your view, the "0" mark will take the shot as you see it, move towards the + sign and you are letting in more light and the - sign less.
Should you always perfectly expose your pictures? Easiest! NO! The exposure levels lets you tell a story, if you think about what you are trying to achieve with a shot then ask yourself how does that look? For example if you are taking a picture for the tourist board and the story is trying to attract people to an area then slightly overexpose the shot and make the place look brighter and more exciting. If you are taking a picture for a story about vandalism then underexpose the shot and make it more moody.
There is no right and wrong way but you quickly learn what you like for different situations and in my humble opinion that is what you should develop.