If you find you cant play fast enough with your fingers, it may because you aren't a;ternating properly. If you wanna try and increase your speed, play these over and over again as fast as you can. (Alternating your fingers of course)

2 finger aletrnating
G-------6---4---6------------------------------
D---------0---0---0--6---5---4----2------------
A---4-----------------0---0---0----0--2--------
E-----0--------------------------------0-------
   {1 2 1 2}
       Or
   {2 1 2 1} Fingers. 1 being index, 2 being middle.
G-------9--------7-------------------
D---------0-9--10--0-10-9------------
A---7--------0---0-----0--0-9--------
E-----0---------------------0--------
   {1 2 1 2}
       Or
   {2 1 2 1}
G-------------------------------------------
D-------5-7-5-------5-7-5---------5---------
A-----7-------7---7-------7-5-5-7---7-------
E---5-----------5---------------------------

3 finger alternating.
(When using 3 fingers, always start with your ring finger, its much easier than starting with your index)

G-----------2-4-5-4-2--------------------2-4-5-4-2-------
D-----2-3-5-----------5-3-2--------2-3-5-----------------
A-3-5------------------------5-3-5-----------------------
E--------------------------------------------------------
 {3 2 1 3}Fingering, 3rd being your ring finger.
 (cont.)
G-------------------2-4-5-4-2-------------------
D-5-3-2-------2-3-5------------5-3-2------------
A-------5-3-5-------------------------5-3-------
E-----------------------------------------------
 {3 2 1 3}
G-1-2-3-4-----------------------------------------1-2-3-4-
D---------1-2-3-4-------------------------1-2-3-4---------
A-----------------1-2-3-4---------1-2-3-4-----------------
E-------------------------1-2-3-4-------------------------