A free software that can extract subtitles from a DVD is called VobSub Ripper.
Download and unzip the archive, run the program. In the main window click on "Load IFO..." and choose the source IFO file. Usually it's the biggest IFO file that is associated with the main movie. Let the program analyze the DVD structure. It may take 5-10 seconds. Click on "Save To..." and choose the folder where you want your subtitles to be saved. Click on "Next >".
Choose program chains. Usually for long movies there's only one program chain PGC 1, but for TV series there can be several program chains, each corresponding to a different episode. In this case, you will have to extract subtitles for each episode separately.
Choose languages (I prefer to choose all languages – you never know) and then click on "Next >". The VobSub Ripper will start extracting subtitles. Usually it takes about 2 minutes for a DVD9, if all the files are stored on your local hard disk. It can take about 10 minutes, if you extract subtitles from your original DVD. At the end of the extraction you will have 2 files: idx and sub. These 2 files are most frequently called subtitles in vobsub format.