I thought it would have been good to have taken some pictures but it was after the fact! There really isn't much too it. Sorry for the wordiness!
The boards I have listed are the proper thickness. If you have a table saw, set the fence at 1-1/8" from the blade. I use a ruler and measure from the teeth of the blade to the fence so I have the absolute proper width. It doesn't hurt to run a scrap piece of wood through the saw to check that you have set it accurately.
When you are happy with the setting, run the oak through the first time. Then take whatever is left and run it though again. If you bought the piece from Home Depot in the US the remaining piece should should be close to the right width. This should give you enough pieces plus extra for the entire game. There are really only 4 pieces along the sides of the game and the shooter lane that need to be replaced. The pieces at the top of the playfield are a different width so I didn't bother with them. I used a black Sharpie on the exposed parts of the wood just so it matched the side rails. You can paint them if you like, I was just being lazy.
Take off the apron and the unscrew any plastics that rest on the rails. You'll also have to remove the small nails and screws (you will reuse these) in the metal ball guides on the left side of the game. Measure up the old pieces and cut your new ones to the proper length. The cut pieces will have sharp edges so sand them lightly to smooth them out a bit. Now you have to decide whether to paint or stain them. Taylor suggest spraying a clear lacquer over them as a final coat for some added durability. I figured I could always repaint them or make new ones if they got to beat up.
Tilt your playfield up and start removing the screws that hold each original piece to the playfield. It would be best if you can line up the new piece, mark it though one of the existing holes in the playfield, drill a small pilot hole and then put the first screw in. Once you get one in, you can drill the remaining pilots based on the existing holes. The other option is to use the old piece as a guide. Put it beside the new piece, mark the holes and drill them.
Once you've put all the screws back in you can lower your playfield. You should drill some pilot holes where the small nails and screws were in the ball guides. It will be easier to nail and screw them back in this way. Put your plastics back in position and any other parts (gates, spinner) that were attached to the rails. Drill pilots and replace the screws.
I think that's about it. Let me know if you have any questions.