The first step in any construction job is to first understand what materials go into your project. So, lets take a look and see exactly what is underneath those bricks so that you can understand why you are having problems, and know what your looking at when you remove the bricks.
At the very base of your brick patio is a black landscaping fabric. This fabric creates a barrier between the materials underneath the bricks and the soil.
Over the landscaping fabric is generally 4" to 6" of compacted gravel. This gravel gives the bricks a steady surface on which to lay on, as well as allow the flow of water through so that you won't have standing water on the surface of your patio. Because the gravel is compacted prior to the next step, it should not be responsible for an unlevel patio.
On top of the compacted gravel and just under the bricks is roughly 1" of sand. The sand gives the bricks a level surface to lay on if done right. If you are having trouble with your patio being level, then it is probably due to the sand being unequally distributed over the gravel.
Now that you know where there problems can occur, you will be able to determine upon inspection what steps to follow in order to fix it.
The amount of time required can vary greatly depending on the size of your patio. It is a good rule of thumb however to expect it to be an all day activity if you have the help of a few people, and you have a small brick patio. Otherwise expect it to take a few weekends if you have a large patio or if you do it by yourself.
(1) Rubber hammer
(2) 3/4" steel pipes (needs to be shorter than the width of your patio)
(1) Straight 2" x 4" piece of lumber
A few bags of sand