Your Checklist to gain your Brazilia Jiu Jitsu Blue Belt:
1. Learn a Take Down!! - doesnt matter which one it is. Just try to learn one that you feel most comfortable with and just go for it!
2. Learn One Pass - ideally you should have several types of guard passes that you can chain together to develop a complete passing game but at the white belt level, after a few months of learning and drilling the different passes, choose one and be relentless about going for it.
3. Learn a Sweep - as a brazilian jiu jitsu player you need to be able to work off your back. I would learn and try to drill several sweeps from the closed guard, half guard and any other guard you feel comfortable but at the end of the day you need a GO-TO move. My preference would be the butterfly guard sweep or the classical half guard underhook sweep.
4. Submission - try learning one basic submission to attack. I recommend either the arm bar or the triangle. Both are available from top and bottom. Both take years to really master but you can use these basic attacks at any level.
5. Go to a Seminar - you want to get your belt but you really have not seen any BJJ until you have gone to a seminar, preferably with one of the top instructors or competitors. You will find seminars everywhere on the internet. Pick one and try it out. It would give you a second perspective and its a lot of fun if you go with your team for a few hours to learn something different.
I strongly recommend seminar of more classical jiu jitsu guys especially and white and blue belt levels.
6. Private Lesson - an excellent way to make progress is to take private lessons. At the end of the day it is for you to actually make notes and ask the questions. if you ask the good questions, you will get the information from your instructor that you need to make progress. Take a private lesson every month or two and you will be a much better brazilian jiu jitsu player.
7. Compete! So you want your next belt huh? well you need to deserve it! you may have been training for a year or two but only in competition can you really find out where you are on the food chain. Compete as much as you can at white belt, gain confidence and it will be a matter of time before your instructor just hands to you that long awaited blue belt
I would say that typically it should take at least 2 years to gain a blue belt training at least 3-4 times per week (consistently) but the reality is that if you actually want to get good at this sport you need to train as much as you can.