Weaving in the end makes it plenty secure, and is nice and stretchy too. Basically weaving in turns that loose end into part of the fabric. There are several good ways to weave in; somebody mentioned a good tutorial in the knitty.com archives.
How much to cut off? Well, you will probably need several inches to weave in, if you use the weave-in method that has you follow the contours of your stitches, and then you will need enough extra that you have some leeway for maneuvering the tapestry needle, so maybe between eight and twelve inches total depending on the thickness of your yarn. At the end of the weaving in process you just can cut off whatever you feel is excess.
Hope that helps!