To watch a replay you have to put the file in the appropriate folder in your Sins user path (C:\Users\youruser\AppData\Local\Ironclad Games\Sins of a Solar Empire). There are folders for SP/MP autorecords, and SP/MP manual records. Put the file in the proper folder, launch the game, go to Single Player > Watch and pick the replay (same as the file name).
Note that your game's version needs to match the version the replay was recorded on - the replay file is basically a collection of all the actions taken in the game and when you play it you're actually re-creating the game as it happened, so the versions need to match. Likewise, you can't watch Entrenchment replays without having Entrenchment for the same reason.
