Beauty, I'd love to find that deal. The price tag suggests that there may be more issues than a bad transom.
I won't suggest I can tell you how to do it without seeing the boat, but you basically remove as little as possible, the motor, cap and all through hardware inside and out, and slide the old one up and out. There was a sheet of aluminum over the interior surface in mine. It came out with the wood and can go back in from the top. Using the old wood (or whats left of it) as a template, trace and cut out the new one. I used plywood in different widths to stack up and get the original width. I bonded them together with liquid nails, clamped overnight and then painted everything.
BTW, take note that the exterior grade painted plywood from the factory lasted until now, so painted exterior grade plywood should last 20 plus years. Using that school of thought and considering my budget, I used Auruco plywood from Lowes and porch paint. If mine lasts 25 years I'll be 88 years old the next time I pull it apart. I don't think there is a thing wrong with using the same material and techniques as the factory to put the boat back together.
Clean the old slot out like crazy, get every scrap of everything out and dry fit the new transom, including the cap and inside sheet. I painted the interior of the hull with the same paint as the transom let everything dry for a day and put it back together, with a somewhat different stern configuration. I used all stainless hardware throughout the rebuild, but again because of the budget, I reused the old stainless hardware when it was in good shape.
I do see that my signature is back, I thought I must have done something sometime that deleted my sig.