Below are three methods I use to tune a 6-string  
guitar in the usual E A D G B E fasion.
  In general, it's better to tune up to a note 
(not tune down).  This means that if your string 
is slightly sharp, you should tune it slightly 
flat before trying to get it right where it 
should be.  This gives you better resistance to 
slipping.
  For notes that are very slightly sharp, often 
simply "streching" the string will put it right 
in tune.

Method 1: Same notes (most common method).
Push the fret number of the indicated string.
(1) E -> 5, A -> 0
(2) A -> 5, D -> 0
(3) D -> 5, G -> 0
(4) G -> 4, B -> 0
(5) B -> 5, E -> 0

Method 2: Octave notes.
This lets you strech the octave string to see 
how far to tune it.  For me it's more useful 
than method 1.
Push the fret number of the indicated string.
(1) E -> 0, A -> 7
(2) A -> 0, D -> 7
(3) D -> 0, G -> 7
(4) G -> 0, B -> 8
(5) B -> 0, E -> 7

Method 3: Harmonics.
Place your finger on top of the string directly 
above the fret indicated, but don't press the 
string down.  Pick the string closer to the bridge 
to get stronger highs.  This isolates a "harmonic" 
tone of the string which is higher than the 
fundamental.  Our ears are more sensitive to 
tuning at higher frequency so this helps spot 
tuning problems better.  This method won't work 
well on a guitar with poor intonation (use the 
octave method instead).
(1) E -> 5, A -> 7
(2) A -> 5, D -> 7
(3) D -> 5, G -> 7
(4) G -> 4, B -> 5, E -> 7