First, go to feedback.tf2maps.net. Find your map and click the title to go to the feedback page then click Demos. You'll see a page with one or two links that will download a .dem file of when the map was played. Place that file in your Steam/steamapps/common/Team Fortress 2/tf folder. In game, open the console and type "playdemo (demo name here)". That should just about do it!
Keep in mind that even after a game is finished, it can take up to 30 minutes for the demo download to appear on the site.