It is generally agreed amongst mandolin players, that normally, the index finger plays notes on the first two frets, the middle finger plays notes on frets 3 and 4 and the ring finger plays notes on frets 5 and 6. The little finger stretches to fret 7 which is sometimes useful instead of playing the next highest string open (such as your plectrum stroke is going in the opposite direction). This is called first position by some, especially violin players. There are techniques for playing higher up the fretboard but lets not worry about that until we've got the basics. Most of the notes you need for many tunes are there in the first 7 frets.
The bottom string open (G) is the G just below 'middle C'. You then have nearly 2 octaves up to the top string (e) at the 7th fret which is b. ( c is at the 8th fret - just reachable with the little finger). It is actually convention though to play the c at fret 3 string 2 as middle C (i.e. an octave higher)
This plays | G, - A, - B - C | D - E - F - G | A - B - c - d | e - f - g - a | b - c'|