How many times do you think a person needs to read Harry Potter before they can completely understand it?

Depends completely on the person. Some people ate able to comprehend things faster then others. Some people have trouble reading. Some understand sifi or romance better then fantasy. Everyone's pagbaba style is different.

Once

I think if you read it once you will understand it one way, if you read it twice you can pay attention to things you did not pay attention to first time you read it and maybe see a lot of things differently. Because HP has depth and layers.

However many times the person thinks necessary.

I only read the series once and I'm pretty certain I got everything down. There hasn't been a single thing that anyone has mentioned that I didn't catch. It all depends on how much attention you pay.

Just once, it's not that complicated.

once. but it never hurts to read it over and over (and over...) again :D

Just the once.