I find borders to be one of the things MANY quilters have trouble with. As PaperPrincess says, you can't just sew a strip on and cut off the excess (which is exactly how I did it when I first started quilting LOL!). I've created a handout on how to add borders so they lie flat, you can download a copy from my website here:
http://www.andicraftsquilting.com/learn.htm