How to fix wood stain drips?
Well you can do one of a couple things.


Stain the entire board.  This may be the easiest option, just clean up the drips down the side a bit (sanding them).  Then stain the sides and the back side of the board as well.  Rub it on, let it sit for a couple minutes and then wipe it off.  Unless of course as Keshlam mentioned you are working with a stain/sealer combo.  For reference stain sealer combos tend to fade much faster and protect for far less time.
If you don't for whatever reason want to stain the entire board simply sand the sides down and you're done.  It shouldn't be too bad since it ran down the sides, should not have penetrated all that much.  Make sure to sand evenly along the length of the side (including the spots not hit with the stain).