I tend to only block those quilts that will be hung either as a wallhanging or in a show--but I don't do big time shows, so even with local fair and guild show I sometimes don't block, especially if it's a bed quilt.
That being said, I will use a cork board to pin the smaller projects onto and with larger quilts, I will lay out a sheet of plastic on the basement carpet, and then pin the quilt to it (and carpet) and set a floor fan to aid with drying (I also run a dehumifer in basement in summer). I try to block with as little water as possible--so will use spray mist for most. Occasionally will put one into filled washing machine and then spin to get excess water out--but make sure you've done a seam around the whole outside first! I also have learned that it is much easier to block BEFORE you bind.
Even when I have worked to keep my quilt square, sometimes with heavier quilting, blocking is necessary to make it hang flat. Remember , besides pulling it to square, you can also "push" excess back into square.
Also, I know some think that you can just lay a square on the corners and check for it being "square"--but I know from time spent on a drafting table that a t-square will look square even when it isn't if there's not a solid, square edge to judge it from. For this reason, with larger quilts I always take measurements and square from that, not just laying a ruler down .