The mandolin has eight strings arranged in four pairs of two (a pair of strings is known as a course). The stings are tuned G D A E (G being the lowest). This can be remembered by the rhyme Good Dogs Always Eat.
I normally tune the strings in the order A,E,D,G. You can tune the strings by ear or by using an electronic tuner.
To tune by ear you can use a pitch pipe or tune to another instrument like a piano or accordion. Turn the tuning pegs until the two instruments sound in tune. Which direction you turn the tuning peg will depend on whether your strings are higher(sharp) or lower(flat) compared to the reference tone.
One you have one course of strings in tune you can then tune the other strings to that course. For example if you have the second course (A strings) tuned then you would follow the following procedure to tune the rest of the strings.
Step 1: Play the 7th fret of the A strings. This gives the E note which should be the same as the E strings(1st course). Tune one of the E strings to the 7th fret of the A strings. Then tune the 2nd E string so both E strings are in unison.
Step 2: Play the 7th fret of the D strings. This gives an A note which should be the same as the A strings (2nd course). Tune one of the D strings so that when the 7th fret is played it is in tune with the A strings. Then tune the 2nd D string so both D strings are in unison.
Step 3: Play the 7th fret of the G strings. This gives a D note which should be the same as the D strings (3rd course). Tune one of the G strings so that when the 7th fret is played it is in tune with the D strings. Then tune the 2nd G string so both G strings are in unison.
Chromatic Tuners can also be bought from any good music shop and via the internet. These have a visual display that shows you when the strings are in tune. These are useful when playing with other people as it keeps everybody in perfect tune.
The strings on a mandolin should be replaced regularly. How often you replace them really depends on how much you sweat(!) when you play and how often you play. After time the strings will become tarnished and sound dull.
Restringing a mandolin can be difficult mainly due to the high tension in the strings and also the fact that some mandolins have removable bridges. The following site has good tips on how to change the strings