Funny story - they cut the wrong carpet. I didn't pick this actual carpet. But it was already done, and I still liked so we just went with it.
We actually opted NOT to use any type of padding or glue, just in case this space were to get wet. It is, after all, and enclosed porch. We have never had any problems with water getting in, but you never know. So the carpet is literally just cut to fit and then plaid in place. So far, its been a few weeks and this hasn't been an issue at all.
After that it was just a matter of moving everything in and getting it put into it's place.
So there you have it - our playroom progress. It took us 9 months to get there - but it is finally a nicer place to play!