My mother is completely deaf without her cochlear implant, so closed captions and subtitles on DVDs are standard fare in our house. However, when I make a home movie, I haven't always had a way to subtitle it for her. You can make a video with captions that are part of the video itself, but I could find no way to turn them off -- until I found SRT files and learned how to author a DVD with them using open source tools.
SRT files, created by the SubRip project, are formatted text files that contain information on subtitles and captions for DVDs. With the right tools, you can use them to make a captions that play on a standard DVD player.
The overall process is simple. First, make sure you have a fast computer with lots of memory, hard disk space, and a good DVD burner, because working with video and audio is a resource-intensive process. Load your video file into a milliseconds-accurate video editor such as Cinelerra and get the time indexes for each phrase of dialogue. Enter the dialogue and the time indexes into the SRT file, then integrate the SRT file into a DVD-compliant format and burn it to disk.