Here's the intro to the Gravedigger Blues. You should be able to play the bass line for the whole piece with your thumb, and use your index, middle and ring fingers to pluck the chords and licks. Much of the piece utilizes the Dead Thumb technique which I discuss in my Dead Thumb lesson.
If you want some tips on building accuracy and speed with you right hand fingers, check out my lesson called Feel the Strings.
For the purposes of this lesson I will refer to your fretting hand fingers as 1=index, 2=middle, 3=ring, and 4=pinkey, and your picking hand as T=thumb, i=index, m=middle, and r=ring. The first two measures should be self evident. Fret the C# in measure three with your 2 finger so you can slide up to the D# and use 3 and 4 to fret the E and E# respectively. This way your 2 finger is free to fret the G# on the first string and 1 can fret the C# in the bass, as well as the bass descention that follows it. Measure four is a little tricky. Fret the F# in the bass with 1, then the G# with 4, and use 2 to do the pull-off and hammer-on sequence on the first and second strings. Then use 1 to to fret the A# in the bass on the third beat, and 3 to fret the F# on the first string. Use 4 to hammer-on to the G. In measure five we have a chromatic descention. Use i and r to pick the third and first strings, and use 2 and 3 to fret them. This way you can use 1 to fret the C and B in the bass when you get to them. The C has to be cut off a little, as is indicated in the tab. Then use 4 to fret the G in the bass.
You may have noticed that I called the note on the third beat of measure three an E# instead of an F. This is because of the context of the chord. The chord there is a C# major, and it is spelled C#, E#, G#. This is called a secondary dominant chord, a V of ii. For more info on that subject, check out my article called Chord Progressions 201.
Likewise I will refer to A#'s rather than Bb's. These are called enharmonic equivalents, different names for the same pitch. A# makes more sense in the key of E than Bb. The intro utilizes secondary dominants to get that bluesy but non-typical sound. The progression is: E, G#, A, A#dim, for the first two bars, and E, C#, F#, B, E in the next two bars. These are standard blues progressions, and the second is commonly referred to as a VI II V I progression.