Using the tutorial created by DanTwoLakes, I pressed the pieces flat. All it takes is a good iron, a flat surface, and a bit of time. First I soaked the pieces I wanted to press in the bathtub for about 20 minutes. The felt backing on this vinyl soaked up water faster than you can say boo. I set the iron on its highest setting and let it warm up.
You probably shouldn't use your wife's good iron or ironing board like I did. Irons are found all over at yard sales and thrift shops for a dollar or two. I have two irons out in the garage that I use for various things, but I didn't want to use either of them because they have heat activated glues on them. Looks like I'm buying her another new iron tomorrow, and I get this one. I at least covered her ironing board with an old flannel sheet, so the pad didn't get messed up.
Starting at one corner, I slowly pressed it flat. Keep the iron moving - don't let it sit for more than a second or two in one place. If the spot you're trying to iron dries out, either move on or rewet it. It's the steam created by the iron on the wet fabric that flattens it, not so much the heat from the iron itself. If the vinyl's too dry, you can iron it all day and it won't have any effect at all. You're not going for perfection here - a wrinkle or two isn't really going to matter much. What you're trying to do is flatten the piece, especially the seam allowance, so that it can be used for an accurate pattern.
I didn't soak or try to press the inserts. They're backed with foam to create the pleats, and soaking all of that foam would have been a royal mess. I'll just flatten them out using weights when I trace around them.
Picture 1: The wet piece of vinyl on the ironing board. Donâ€™t try this over a carpeted floor - it WILL be dripping all over the place.
Picture 2: With the iron nice and hot, on it's highest setting, I kept it moving as I pressed out the wrinkles.
Picture 3: The first finished corner. This is the big rear panel of the seat back. I did the rest of this panel, the boxing, and tail of the seat bottom the same way. They're all outside under some weights to flatten them a bit more.