WORKEROUTER
Master Don Juan
Probably the best things to study would be:Kerpal said:The guard is a form of "damage control". If you have to be on the bottom, it's much better than being in a knee ride (knee on stomach), side control (opponent on top perpendicular to you), mount (opponent straddling your chest), or rear mount (opponent on your back with legs wrapped over your waist). I would NEVER purposely go to the guard in a real self defense situation but if I had to be on the bottom, the guard is the best position to be in.
From the guard, you have some control over your opponent's body and you have sweeps, submissions, you can transition to a better position (ie going around to the guy's back and choking him or just getting away) and it's a lot easier to get to your feet because you can use your legs to push the guy away and make space. You also have a much easier time defending against punches. From all other positions, your only option is to try to escape, and it's a lot harder and the other guy has a dominant position on you where he can go for submissions (unlikely in a self defense situation I think) or strikes.
The guard is only 1 part of BJJ though. Like Workerouter said, if you just want to train for self defense purposes you don't need to learn a lot of the "fancier" moves because those are mostly for use against people who have some training in BJJ, I highly doubt you're gonna run into a BJJ guy in a dark alley though. You would be amazed how well it works against someone who doesn't have any training though.
-escapes from the bottom
-controlling the opponent from the top (knee on stomach, mount)
-escaping the common chokes and holds (guillotine, bear hug, etc)
-throwing simple, quick, effective submissions from all angles
I've used BJJ on a couple occasions. One time I got caught with a barrage of drunken punches...quickly took him down with a double leg, went to mount, and proceeded with an arm bar. Other time I got bull run by a bigger guy trying to take me down...went down with him to the ground, locked my legs around him, guillotined him and arched my back up. One time I got caught in a guillotine by a guy while drunk. Used the basic trip escape and assumed a side mount escape, then applied a basic key lock.