Tuning is a skill which improves the more you do it. Relying solely on your digital tuner will not help things. Sure, they are the only way to go   for a quick, between  song adjustment, but they do not improve your sense of pitch - which is an important skill for any musician to develop. Try and do things without your tuner first, and then check your accuracy against it.

Tuning the First String
Start by getting a reference E note from another instrument, such as a piano or pitch pipe. Failing having another instrument at hand, use your tuner, but only tune your low E string for now. Play the reference note first, then the string you want to tune (in this case the low E string), because your ear "fixes" on the first note you hear. If you play the string first, your ear pitches on that, and it makes it more difficult to identify the second note as the correct pitch.

Now listen. This is the hard part, because you have to learn what to listen for. If the two notes are grossly out of tune you should be able to identify whether your string needs to be flattened (lowered in pitch) or sharpened (raised in pitch).

Now here is the "trick". When you get the two notes close to unison (the same note) you will begin to hear a "beating" sound, where the volume goes up and down in a pulsing pattern. (Those of you with electric guitars - try this with distortion on the guitar and it will be very pronounced.)

The closer in pitch the two notes are, the slower the beat frequency will become, until you will not be able to discern any audible beating. Viola! The two notes are in tune. Now using your newfound knowledge tune the other strings with one of the methods below.

Method One
If you fret your in-tune Low E string at the 5th fret, you will be playing an A note, which is coincidentally the same as your open (unfretted) 5th string. Play the note on your 6th string first, then follow it with the open 5th string. Once again follow the tuning proceedure outlined above, listening for the beat frequency. Now do the same with the other strings as per the diagram below.

Method Two
Similar to Method One, but using harmonics on the 5th, 7th and 12th frets to tune all strings but the second (B) string. The B string can be tuned using Method One. This is a good method, as harmonics are purer notes, containing less overtones.