The rules for Tic Tac Doh! instruct that it be played on an imaginary 3x3 grid. This specification is important, because the first player can only control the size of the first piece, not it's position (center, edge, or corner). The second player may determine the full location of the board by playing a piece two diagonal spaces from the first, but usually it's not until the third turn, or even later that the imaginary board is fixed around the pieces.
I don't find it hard to visualize a 3x3 grid of the proper size, nor to assess the relative positions of pieces played early in the game. But I do understand people wanting additional visual clarity. These next two photos show incorrect ways to play Tic Tac Doh! on a board, and there have been comments on the image pages to point out the fact that as shown they are imposing constraints on the play that are alien to this game--and, in my opinion, seriously weaken it.
However, it's fine to play on a grid-style board, as long as you observe two cautions:
1) The grid must be at least 5x5. A Volcano board (like the one in Pyramid Arcade works great.
2) The first play must be made on the center square of the grid. (If there is an even number of squares, one of the two or four central squares will be fine.)
Then play as normal.
Here is a "board" consisting of a tiled tabletop that doesn't restrict positioning of the nine-square grid:
Here is a Volcano board, where the first play was in the center square, and the second was in one of the corners: