First of all what is the difference between tablature and written music? Well written music shows you which notes to play and for how long, that's all. Music written for classical guitar also uses extra symbols to hint to where on the guitar neck to play the notes and which fingers to use.
Guitar tablature shows you where on the guitar fretboard to place your fingers for each note you play. Often tablature is not so good at showing rhythm, but often you know what the music is supposed to sound like, so this isn't a problem.
Guitar tab is written on 6 lines. One line for each string on the guitar, with the thinnest E string at the top, and the thickest E string at the bottom. Like this:

If the guitar is to be tuned diffently to the usual EADGBE, the tab will usually show this.
Notice the bar lines, they indicate the end of each measure. Often the time signature will be shown, this tells you how many beats there are in the bar, for example 4/4 indicates that there are four 1/4 notes (crotchets) in the bar. The following example shows the scale of G major played in quarter notes:

So you play the first note at the 3rd fret on the 6th, or low E, string. Then you play the 5th string open, then place a finger at the 2nd fret on the 5th string to play a B, and so on. Which finger to use for fretting? This is based on 'position' in this case we are playing in first position so use the index finger for fret 1, second finger for fret 2, ring finger for fret 3, and pinky for fret 4.
Tab can also show you when to slide, bend a string, hammer on and pull off. For example to slide from the third fret on the second string to the 5th fret on the second string:
Sliding
You should take 2 quarter notes to slide from the 3rd fret to the 5th fret and then hold the note for two more quarter notes.
Hammer On and Pull Off
In this example play the 1/8th note at the 2nd fret of the first string. Without picking the string again hammer your third finger at the 3rd fret to sound the second 1/8th note. For the pull off, have your pinky on the 5th fret and your second finger at the third fret (this is second position), pick the first string, and after 1/8th note pull you pinky off, plucking the string slightly.
String Bends Part 1
OK, these are a bit tricky to follow and you will come across lots of other varieties. Often you'll get the feel for the riff from the tab, but by listening to a recording you'll hear what you are trying to do.
In the first bar you play the 1/4 note at the 5th fret and bend the string to raise the pitch by one tone (to make the same sound as playing the note
at the 7th fret. The total note length is two 1/4 notes. You will see bends for 1/2 tone, 1/4 tone too. Often the bends are up to you to interpret and play the way you want.
The second bend in the first bar is slightly different, you again bend the note up one tone, but just before the end of the two 1/4 notes you let the bend off to lower the pitch again.
Strum PatternsTab is often used to show strum patterns. To be honest these are often difficult to read. You need to be able to read rhythm from standard music notation. So the easiest way is to learn the chord changes and then listen to a recording.
Here is a simple strum pattern shown in tab:

This is an Am chord with the open 5th string bass notes palm muted (hold the palm of your right hand lightly against the string as you play the note to stop it ringing out). The little arrows show up and down strokes with the pick. This pattern could be the opening to One by U2, but of course it is just one chord, so there's no copyright issue...
Talking of which it would be nice to finish with a short piece of tab you could try. Copyright could be an issue, so here is a small piece of J. S Bach. A Bouree in Em, often played by Iain Anderson of Jethro Tull, many years ago...