XBMC, and hence Raspbmc, can automatically show subtitles when the subtitles file has the same name as the video filename and is placed in the same directory. What is awesome is that you can download and play subtitles for any video file right from the comfort of your XBMC!
XBMC 13 (Gotham) and later
XBMC 13 added native support for subtitle downloading. Go to Settings > Video > Subtitles. Scroll down to Default TV service and Default Movie service. When you enter, you are given a list of subtitle websites and you can pick which you want for TV and movies. More details can be found here.
XBMC 12.x and older
First, you need to install the XBMC Subtitles add-on. To do this, go to System > Settings > Add-ons > Get Add-ons > XBMC.org Add-ons > Subtitles, choose XBMC Subtitles Add-on and install it.
Next, play any video file. While it is playing choose the Download Subtitles option. This is available in XBMC remote apps like Yatse. Else, choose whatever option makes the video playback scroller appear. There on the set of icons below it on the right side, pick the first one.
Either way, this takes you to the Downloading Subtitles widget. XBMC will query subtitles databases online and show you a list of the best matching subtitles for your video file. Pick the one you want and press OK. XBMC will download the subtitle file and restore playback of the video file with the subtitles enabled. It is as easy as that! :-)