Hi gim0,
To obtain PADI Open Water (OW) certification you need to do knowledge reviews, an exam, confined water dives and open water dives.
When you sign up for a course there will be a package including a textbook. I would recommend getting the book ahead of time, read it and answer the knowledge review questions. If you do this, the classroom portion will go faster and you will be able to spend more time talking about the pool and open water portions.
In the pool you will do 5 dives. During this time the Instructor will demonstrate the skills and have you practice them. This is the time to ask for help and resolve any problems you have.
In open water you will essentially be demonstrating the skills you learned in the pool.
At my shop we have a classroom session Friday evening (knowledge 1), a classroom session Saturday morning (knowledge 2 & 3), a pool session Saturday afternoon (pool session 1, 2 & 3), a classroom session Sunday morning (knowledge 4 & 5), a pool session Sunday afternoon (pool session 4 & 5). Next weekend we have Saturday open water dives 1 and 2, Sunday open water dives 3 and 4.
If the classroom portion went well (everyone studied before the class) we could problem do it in one day. I don't believe there is anything saying you cannot then do all the pool work in one day. However, you cannot do more than 3 open water training dives per day. Since there are 4 open water dives, you might as well do it dive 1 & 2 one day, dive 3 & 4 next day. This means 4 days are possible.
Something to consider, there is a minimum requirement for certifying someone. If you insist on a 4 day course, you are probably going to get the minimum training. The more time you give the instructor, the more of their knowledge and experience they can share with you.
If you still want to do it in 4 days, consider private instruction or find someone with a reduce class. An instructor can do 8 students at a time. If the class is full, you will get 1/8 of the instructor's time. If you have a one-on-one session, you get 100% of the instructor's time.
Darrell