You can't even start on this puzzle until you talk to Wade and tell him about seeing Harper.
When you do, he gives you "Wade's Note" that gives you the general rules of the game. Read to the end of this hint for a screenshot of the solution.
The general goal here is to place those red and blue battery-like tiles in the grid so that each row and column has the number of red and blue pieces shown by the numbers at the left or along the bottom.
For example, in the Amateur puzzle, the top row has a red 3 and a blue 4. That means the top row will have three red pieces and four blue pieces in it.
The other rule is that the red end of a tile can only touch the blue end of a tile -- positive to negative, like batteries.
To place a tile, click in the slot where you want it to go. Click again to flip it (red for blue); click again to replace it with Xs (meaning that slot will stay empty). One more click returns you to an empty slot.
Since the whole puzzle is 8 x 8, you know that any row or column that's 4,4 will be completely filled. As soon as you get any one tile in that row or column, you can fill in the rest of the row (or column).
When you get a row or column where the numbers have been X'd out, it means that row or column has all the tiles it's going to get. If you're completely sure all the tiles are correctly place, the rest of the tiles that intersect that row or column can be assumed to be empty.
Other than that, it's part guess, part logic. If you put in a piece and find it clashes with other pieces, well, something's wrong with the layout.
Annoying? You bet. If you'd like a little jumpstart --
-- I'll tell you that the first column at the left is completely full; for Amateurs, it's red on the bottom and blue on the top; for Masters, it's blue on the bottom, red on the top.
Still completely stuck? Yeah, I don't blame you. Here are the solutions:
-- and "Charlotte's Sketch," which you won't use till very close to the end of the game.