In the beginning, focus on the fundamental positions of BJJ and learn how they are connected. In the beginning sparring can be very confusing, it helps if you can recognize where you are and where you want to go to.
Once you know the positions, learn the techniques from the fundamentals curriculum. Sparring will become less chaotic and you can now use technique to improve your position.
Learn to relax under pressure. Focus on learning instead of winning (this will keep jiu jitsu fun).
The time as a blue belt should be used for exploration. If the fundamental positions are the cities on a map, it is now time to explore the villages.
Watch as many instructionals as you can. Pick a position, learn all the moves for a few weeks and then move on.
A blue belt will often have an advantage against a white belt because he knows more techniques and positions.
When you reach purple belt, you will be at least somewhat familiar with most techniques. If you want to keep winning against other purple belts, you have to take a different approach.
Now is the time where you build your own game. Start with your favorite position and work on technique combinations.
BJJ becomes like a chess game. You want to stay a few steps ahead of your opponent.
A purple belt will often have an advantage against a blue belt because he sets up traps and combines techniques.
A brown belt should have a very good understanding of the fundamentals. At brown belt you should fill the holes in your game and work on the positions that you used to ignore.
A brown belt will often have an advantage against a purple belt because he makes fewer mistakes.
Stay humble, keep learning and train for life.