The flippant answer, Spendius, is (a) pencil and paper, (b) high-lighters, and (c) lots of correction fluid (white-out). Very low tech.
(As an aside, do any of you know who is credited with inventing white-out?)
I have 25 columns across the paper in plan format. Each of the 20 players, from Mysteryman and Osso on the far left to Rhys and George on the right, gets precisely 3/16ths of an inch. I use the remaining 5 columns for ESPN, CoinToss, and how we split on individual games (projected and actual results).
I list the games for each week in as many as 16 rows, along with a couple others for predictions of the final score and room for me to make note of how we are doing ahead of the Sunday and Monday night games.
I have to make a couple of copies of my form each week.
Despite the rules regarding allowing players to make changes, they rarely happen. Changes are not at all inconvenient.
What would be inconvenient is players not making selections. Of the 20 players, 17 have chosen in every game. It is a lot easier to calculate the standings if I can use a uniform divisor.