First off, enable combat logging:
Preferences -> Combat Logging -> Enable Combat Logging
Now download the MOX Parser. But since i can't post a link for some damn reason, Google "swtor Mox parser" and you should find it.
Unzip the downloaded file to a convenient location and run the "RunParser" application. Now you're going to need to determine the location of SWTOR's exported combat log, and tell the parser the location via the Log Location field at the top of the program.
C(varies):\Users\UserName(varies)\Documents\Star Wars - The Old Republic\CombatLogs
Once the program opens, open the Raid tab (or just hit Start, if you want to run solo). Here you'll need the Raid Key, which changes from time to time so just ask someone for it. Ignore the Leader Key input.
Once the raid key has been inserted, click the "Sync to Raid" button on the right. You should be synced to the raid. Occasionally the data will take a while to refresh, so check back after killing some trash.
If you want the overlays, you'll need to be playing in SWTOR Fullscreen Windowed mode. The various overlays can be enabled via the "Pop-Out" drop down menu in the parser program.