In general, you should assign one finger to a fret. Start with your index finger on the first fret, your middle on the second fret, and your ring finger on the third fret. This is known as first postion.

When you play a note on the first fret, keep your index finger in place on that first fret. Then use your middle finger to play a note on the second fret. Notice that leaving your index finger on the first fret gives you added leverage. In addition you will not be wasting effort by removing it. Also, if the music calls for a return to the note on the first fret you are already in position to play it! The point is to take an overview of the music you are playing to get an idea of the most efficient way of dealing with it.

When you play any given fretted note you also want to arch your finger so you don't mute any adjacent strings that should be able to ring clearly. Sometimes it is desirable to mute strings on other strings. But that is a topic for later and more advanced playing skills.