I don't typically measure if I'm using one fabric but I usually have a good idea of what the quilt was supposed to turn out to be and how much yardage I need. Whenever possible I prefer to cut along the length of the fabric for a solid piece, "measuring" it along the bed of the quilt and then adding a couple of inches, but sometimes I don't have enough length for that so I will piece it if needed, that's usually cross grain. I prefer to miter my corners if I can. When I use corner stones, I still only rough measure and then trim the extra length along the edge line of the quilt, so typically I'll put the top on first, cut to the edges. Then piece the cornerstones to the length, put that on the one side, trim off the bottom. Then it's the bottom corner stone to the bottom piece, trim to the edge again. Finally the last side, starting with the cornerstone again and trimming down (keeping the seam line in mind), and fitting in that last corner. Sounds more complicated than it is.
I do a lot of pinning, both with piecing my blocks and putting on my borders, about every 2", far enough down that the pins don't go to/under the foot but enough that it holds my pieces securely, I had more problems with wavy/extra/stretched fabrics when I tried to go pinless. Your mileage may vary but I believe a lot of my success is in a lot of pinning and a lot of pressing.