To follow the play presented in The Checker Maven you need to understand the numbered board and checker move notation.
With Black at the top, White at the bottom, the board is numbered in rows from left to right and top to bottom.
With White at the top, Black at the bottom, the board is numbered in rows from right to left and bottom to top.
These two numbering schemes are of course really the same thing; you are just looking at them from opposite sides.
A move is shown by listing the "from" and "to" square with a dash between them. For instance, 11-15 is the most popular Black starting move; Black moves the man on square 11 to square 15. 22-18 in reply forms the famous "Single Corner" opening; White moves the man on square 22 to square 18.
Captures are shown in the same way. Sometimes a dash is still used, sometimes an x. So continuing our game, Black jumps 15-22 or 15x22 if you prefer; Black jumps the man on 15 over to square 22 (capturing the White man on 18).
Multiple jumps, such as a double or triple jump, require you to pay attention, as the convention is to just show the start and end squares and not the in-between or intermediate squares. So the notation 1-3 would mean a King does a double jump from 1 to 10 to 3. The intermediate square is only shown if there are two ways to jump and it would not be clear otherwise.
In practice this is all very much easier than you might think, and you can learn the numbers with a couple of hours of practice. Some people prefer using numbered diagrams or a numbered board as a "helper." It's your choice, but we feel in the long run you are better off taking the time to learn the numbers, and avoiding long-term reliance on numbered boards and diagrams. Really, it's a piece of cake.