When I am putting things together I try to keep the pieces a similar size as much as I can. That is, put half a quilt with half a quilt, not one row on most of a quilt so that makes putting on borders smoothly a bit of a challenge. I pin a lot... about every 2". I use long quilting pins and pin well below the seam line so that the fabric is held securely but no pins in the feed dogs or under the needle. I really believe that my good results come from pinning and pressing all the time every time. I've tried other techniques and I've seen people who do great things without pinning -- but they aren't me and I'm not them!
With multiple borders as already said, you can sew them together and then miter or put in a corner block.
One other thing that hasn't been mentioned yet is with butt joints you can lessen the number of times you go around a quilt with multiple borders. Let's see how well I can describe it:
First attach the first border to the two opposing sides to the "bed" of the quilt. Then sew the two borders together for the remaining sides, and attach them to the bed. Then you attach the final long borders.
Ideally I want to (a) miter or (b) go around more like a log cabin but there are times when I only have so much fabric and don't have quite enough for the long sides and I'll use that technique. I'm happiest when it is a small print fabric and the seams do their disappearing trick, but I've also had to do it with solids. Less happy but always happy to get the top done!