Each person has their own way and this is mine.
I lay the top out on the floor using my large builders straight edge and square. I then lay a boder piece across the middle of the quilt. The first edge I line up exactly and pin it real good. It helps to stick the pins straight into the carpet so it holds the border and quilt in place.
I very carefully lay the border across the quilt, not stretching or pulling at all, just lay it on the quilt and smooth it gently. On the other side I pin it to the quilt. I then took my little 6" square and cut the border even with the quilt edge. I unpinned the border and used it to cut the other border the same length.
It's just the nature of a quilt that the edges are longer than the center and when I lay the cut border along the edge there is usually a little bit of fullness in the quilt to be eased in. I pin each edge, pin the middle, and start working on each half pinning the center of the half, the center again, etc. Any fullness I have had hardly takes any finessing to get it the same length as the border. Some tips I have read say to mark the border and the quilt by folding in half, in half again, etc. I don't mark it though.
These pictures have the side borders on and the end bordgers are being done. When sewing them on don't put any tension on the fabric, just guide it and let the machine draw it in.