When first starting BJJ, simplifying things is the name of the game.  You will be bombarded with more details and information than you can possibly hope to keep up with.  What you can do, though, is walk away with some key concepts.  These three objectives will help you more than anything when you are first getting started.

Get on top (and stay on top)
This is the most intuitive for most people, especially anyone with a wrestling background.  Even if you didn’t wrestle competitively in high school or college, you probably at least wrestled around with your friends or siblings at some point.  The main concept is one that is simple:  gravity aids your movement, while it restricts the bottom person’s.  If there are punches involved, they are aided by the force of gravity.  If you’re only grappling, holding your opponent in place simply involves pinning him or her against the ground with your body weight.
Staying on top means not pulling the guy into your guard when you’re in his guard.  Yes, weary novice grappler, this practice is indeed frowned upon not only from a competitive standpoint (you typically give up points when you “sweep yourself”), but also from a fighting standpoint.  Stay on top and let gravity aid your positional progress!

Always face your opponent
If  “get on top” is the simplest piece of advice for wrestlers to pick up, and perhaps the most intuitive for everyone in general, “always face your opponent” is the toughest for many people to adapt to.  It is very difficult for most people to get used to the idea that lying on your back is better than “turtling” (turning away to your knees) when on the bottom, but imagine for a moment a scenario in which you and I are having a knife fight.  We start our absurd duel to the death facing one another.  The fight seems pretty even, right?

Now imagine a second scenario wherein I walk around behind you.  On the count of three, we begin trying to stab one another.  Who will most likely win?   The same is true with jiu jitsu:  if you can get on your opponent’s back, you are winning the positional battle.  Never give your opponent this prime opportunity for free!

Get your legs around your opponent
Say whaaaaaaaaaaaat?  You want me to do what?
Initial awkwardness aside, the incredible efficacy of the guard is perhaps the thing that most separates Brazilian Jiu Jitsu from nearly every other martial art.  If you can’t get on top, you had better use your legs to create space and angles in between you and your opponent.  When you’re on top, the converse is true:  your objective is to get around your opponent’s legs as quickly and efficiently as possible, establishing a dominant position such as side control, the mount, or knee on stomach.  From there, just as from the guard, your odds of finishing the match with a submission go up exponentially.