Alright, it took a bit of poking around (I have XP), but I found how to do it in Vista:
Step 1: Make Hidden Files viewable:
I copied this directly from http://www.tech-recipes.com/rx/1521/how_to_view_hidden_and_system_files_and_folders_in_vista/
1. Click the round blue Start thing in the left corner
2. Click Control Panel
3. Click Folder Options
4. Click the View tab
5. Click Show hidden files and folders
6. If you want to see system files as well, unclick Hide protected operating system files (Recommended)
7. Click OK
Step 2: Open the Sins Data Folder:
C:\Users\username\AppData\Local\Ironclad Games\Sins of a Solar Empire\
Where username = your actual user name on the computer. In your case, it might look something like this:
C:\Users\RagingAmish\AppData\Local\Ironclad Games\Sins of a Solar Empire\
Step 3: Open the Desired Replay Folder:
Within the directory from step 2, there are two different replay folders that you may be interested in: Record-MultiPlayer and AutoRecord-MultiPlayer
The first folder contains any replays you saved as a result of clicking "Record" in the menu while playing a game. Most of the time, I never do this, so this folder doesn't contain many files.
The second folder, AutoRecord-Multiplayer, contains all the replays that the game automatically saves whenever you end a game. This is most likely the one you are looking for, so open this one: AutoRecord-MultiPlayer.
Step 4: Find the Correct Replay
Once you've opened the correct folder, you will find a list of all the replays your game has recorded since the last time you deleted them all (in other words, all the games you've played online if you've never emptied the folder).
You want to sort the files by date, so click on the column heading at the top of the page marked "Date modified." This will sort them by oldest-to-newest, or newest-to-oldest depending on which way the arrow is pointing on the heading.All of the record files should be named according to the day and time you played that game, so just choose the file you want to upload.
What I usually do to make sure I have the correct one, is rename the file and then open up Sins. Go to "Single Player" and "Watch." Then change the save type to "AutoRecord MultiPlayer" and watch the replay you just renamed. If it's not the correct one, choose your next guess and repeat the process.
Step 5: The Next Step
Before I move onto explaining how to upload the file onto a file hosting site, I want to make sure know how to locate the correct file. Let me know if anything was unclear so far so I can clarify.
Once you found the right replay, I can explain how to upload it.