Generally, you need to find a legitimate black-belt in BJJ who is willing to promote you. Each such instructor will have their own criteria for blue-belt. Meaning, there is no general answer to your question. You will have to talk to whomever is going to potentially promote you.
At a very high level, you can expect that you'll need to know how to escape from various inferior positions, how to dominate from the top, how to attack from the top, how to pass the guard, how to dominate from the guard, and how to attack from the guard.
The timeframe is pretty consistent from instructor to instructor, assuming you train consistenly 2x-3x/week. It will take you 1 to 2 years to earn blue-belt, assuming no previous grappling experience.
- Kyle