I do longarming and teach soldier quilt volunteers. This is the way I teach it, and the method that works best for me. It always produces perfect borders.
Measure lengthwise center, and both sides of quilt. Add together, then divide by 3, to get average border length (this is important). Cut each side border this length. Lay border on top of quilt, smooth gently, and see which piece is larger, quilt or border? Then pin border on quilt, ends first, then center, then remaining. Now to sew, put larger piece on the bottom of machine, by the feed-dogs. (They will ease in the excess fabric very nicely.) Then sew, making sure you don't pull or stretch anything...let the machine do the work. Repeat for top and bottom borders, including the side borders when you measure.
If mitering the corners, use the measurements as the inside border measurements.
Hope this helps :)