Western music has a twelve-pitch chromatic scale in which pitches are referred to by letter names.  Only seven letters are used, however, because most scales only contain seven notes.  The notes with only a letter name are referred to as natural notes.  The remaining five notes are called accidentals, which are achieved by using a sharp (#) or a flat (b) to raise or lower a note, respectively.  We can see this most easily on a piano keyboard.  On the piano keyboard below, notice that there are seven white keys with letter names and five black keys with accidentals.

You might wonder why the black keys have both a sharp and flat name.  This is because we can get each accidental by either raising the pitch of the natural note below it, or lowering the pitch of the natural note above it.  We call two notes with the same pitch but different names enharmonic equivalents.

The piano keyboard can be used to understand the guitar fretboard better.  Each transition from one piano key to the next key above or below it, whether white or black, is called a half-step.  Likewise, the distance between one fret and the next fret above or below it is also a half-step.  Play your open Low E string and look at the piano key for E.  Now play the first fret on the Low E string.  What is the next piano key above E? That’s right, it’s F.  What’s the second fret, then?  It’s the black key, F#/Gb. 

Use this method to write the letter names of the first four frets on each string of the fretboard.  Why four frets? Because the fifth fret performs the same pitch as the next highest open string.  

The exception is the G string, which performs the pitch of the adjacent B string at the fourth fret, so it is only necessary to write in the G string letter names up to the third fret.  Following this method will identify all the pitches that can be reached near the open strings without stretching the fingers.

Once you have filled out the diagram, practice playing all the pitches in the diagram ascending and descending while alternate picking and naming the pitches aloud.  Use sharps when you are ascending and flats when you are descending.  Repeat this exercise until you can do it without looking at the diagram.  Now you will have an understanding of the pitches you are playing in any chord or melody.