One of the best exercises for your fingers and to work both hands(with speed picking) are chromatics. Theses can be done by any skill level because they are a very simple concept. The will help you with speed picking later on..
Chromatics are notes half steps apart(1 fret) so pick a place to start like in the key of A or something so.. start on the 5th fret of the E string using your pointer and move higher until you reach the 8th fret of E with your pinky(must use your pinky!) then just move to the next string.
Good Luck soon to be shredders!
-Cap'n