Instructions
Add your SRT file to the same directory as your video file. Change the name of the SRT file so that it's identical to the video file name. If the name is different, the PS3 won't register it as an external subtitle file.
Download the PS3 Media Server and extract the files to your computer. Once installed, turn on your PS3 and log into your user account before starting the server on your computer. After a minute the PS3 Media Server should say that your PS3 has been found. If it hasn't, confirm that you have media server support turned on by going to Settings and selecting "Network Settings." Go to "Media Server Connection" and choose "Enabled." Go back to the Video menu on the XMB and choose "Search for Media Servers" if your server isn't listed as an option under Video already.
Open the media server, which will display a white icon with a picture of a PS3 console followed by the name "PS3 Media Server [Computer Name]," and navigate to the folder where you saved your video and subtitle files. If your video name is appended with "{External Subtitles}" then the media server is registering the SRT file for that video. If it doesn't, double check on your computer that the file names are the same. If they aren't, change the name and restart your server
Click the video to start playback. Subtitles will appear without any necessary prompting.