Learning the string names on your guitar is an absolute must; there's no two ways about it. Understanding tones and semitones allows you to figure out what any note on your guitar is. This video hopefully will help clarify these things for you.
Watch on Youtube.
The string names on your guitar are E-A-D-G-B-E.
Some fun acronyms you can use to remember this are:
Eddie Ate Dynamite Good Bye Eddie
Eat All Day Get Big Easy
Eat A Dog, Get Big Ears
Personally I just remember the letter names as is, there aren't really that many of them.
As I said in the video, download the empty fretboard diagram above, and fill it out completely. Practice doing this once per day until you know it. I'm sure it won't take you more than a few days before you start getting the hang of it!
As you become more familiar with the fretboard, start looking for patterns. For example, circle all the times 'A' appears, and see if you can see the pattern. Starting on the sixth string, you simply go up two strings and two frets, and you'll see the octave. That pattern holds true all across the fretboard, except on the B string. What other patterns can you find?
Comments or questions are welcome - just leave one below!