Instead of finding the files then right clicking. Open VLC media player first then left click Media. Scrol down and select open disc. The disc should run as normal allowing you to select subtitles.
If you want to use subtitles every time you can change that in the settings.
How to enable/use subtitles
Before you try to enable subtitles make sure the subtitles you have are in a format that VLC can read! You can find the list of compatible subtitle formats here. If VLC has detected any sort of subtitles available, you will be able to turn them on under the menu: Video->Subtitles track->Track 1
Auto detection of subtitle files uses a 'fuzzy' logic which you can specify. If this is wrongly specified you may end up with more subtitle file options than really exist or miss some that are provided. By default it allows any file in the right place which exactly matches the video name, and may have some extra characters. If you are not seeing the number of subtitle options you expect you might want to allow more 'fuzziness' by changing the preference in video/subtitles/subtitle autodetection where help is available if you 'hover' over the field.
If you mainly use .srt subtitles or .sub, you can get them turned on automatically when they are detected, by setting the Input/Codecs->Advanced->Choose subtitle track to 0, it will automatically turn on the subtitle track. You can also experiment with the Choose subtitle language on the same page. But if you experiment a bit with the settings you should be able to get subtitles turned on automatically.
Note: On Mac OS X, the "Video->Subtitles track" menu item is permanently disabled for some reason. You must manually specify the location of the subtitles file in the "Subpictures" pane of the preferences.