This song is actually really simple. And awesome. 
Note:
F*=(033210)

The song starts with four measures of Am


Am
Spend my nights howling at the moon 
Never wake before noon
    Dm               E
And when the sun it rises 
        Am     G     F
Oh, it always rises soon
          D              E              F*
'Cause I spend my nights howlin at the moon ('ey)

            Am
I never get sleep, sleep, sleep
            F*
No, I just reach, reach, reach
      Dm                        E  
I can feel it on the ends of my fingers
    Am              G          F
And taste it on the tips of my teeth
        D      E            Am
So you see why I never get sleep

Am
Can't get no sleep, don't know why
I Can't get no sleep, don't know why
I Can't get no sleep, no no I
I can't get no sleep

Spend my nights shooting at the stars
Trying to change the world with this guitar
I know it's a long shot
But it's working out so far
so I spend my nights shooting at the stars (hey)

I never get sleep, sleep, sleep
No, I just reach, reach, reach
I can feel it on the ends of my fingers
And taste it on the tips of my teeth
So you see why I never get sleep

Can't get no sleep, don't know why
(Never get sleep)
I Can't get no sleep, don't know why
(Never get sleep)
I Can't get no sleep, no no I
(Never get sleep)
I can't get no sleep

Count sheep! 
I already tried!
Drink whiskey!
Makes my throat too dry!
Smoke weed! (Uh-huh)
Makes my eyes all red
Take a pill, Al!
What, and end up dead?
       Dm                        E
I can feel it on the ends of my fingers
    Am           G          F       
And taste on the tips of my teeth
        D      E            F*   
So you see why I never get sleep

[Chorus]
       D       E           F*  
So you see why I never get sleep
       D       E           F*
So you see why I never get sleep
       D       E           Am
So you see why I never get sleep!