After finding my rear floorboard / carpet soaked behind my driver's seat, I found out on here that it's a pretty common problem. Thanks to the posts and links on here:
Spacecoast post-Rear door water leak…fully explained and solved
Rodpaine's great pictures-Rod's Honda Fit Page

I got the problem fixed with some metal ducting tape. That left me with the problem of how to pull up the carpet so it will dry faster. Unfortunately, I couldn't find anything on that so I tried to figure that out on my own. *Disclaimer* I'm sure there are other ways of doing this, but this took me all of 10 minutes. *End Disclaimer*

I used a shopvac to get as much water out as possible. With the seat locked in the upright position, I removed the two screws securing the seat catch. Then I pulled up the rubber strip on the bottom of the door by hand. I pried the pillar trim piece away from the center trim panel. This allowed me to pry the trim clip in the top/center of the panel. Next I grabbed the bottom corners of the center panel with my hands and applied steady pressure to pull the other two trim clips out. Then I moved the panel piece around until I was able to pull it out.

I pulled the edge of the carpet out from under the panel pieces. Then I pulled the carpet and padding off the bottom of the car. It was stuck a little, but came off without damage by pulling slowly. I used the center panel trim piece to slide under the carpet and padding to prop them up. Hopefully the extra exposure to air will speed up the drying process and get rid of that musty smell.

Since I can't post attachments, I posted a video here: