Travis Picking uses the Thumb, Index, and Middle finger.
The thumb goes on your Base string, and the index finger goes on your B string, The middle finger goes on the E string. 
I like to use alternating Base.   

G Chord                C Chord           D Chord

E---M-----M------------M-----M-----------M-----M---------
B-----I-------I----------I-------I---------I-------I-----
G-------T-------T----------T-------T---------T-------T---
D----------------------------------------T---------------
A-----------T----------T-------------------------T-------
E---T--------------------------T-------------------------

T=Thumb
I=Index finger
M=Middle finger