To answer the original question: yes, a Brita pitcher will soften your water but is an impractical means of doing so for the large volumes required in brewing as compared to other methods.
RO stands for Reverse Osmosis - source water on one side of a membrane is raised to pressure greater than the osmotic pressure which causes water to pass from the mineral containing source side of the membrane to the other where it is collected at much reduced mineral content.
Softening refers to removing calcium and magnesium ions. That is not the goal of a brewer. His goal is to remove bicarbonate. Thus the typical home water softener, which removes calcium and magnesium and replaces them with sodium, is not a good way to treat brewing water.
At your level of understanding I would recommend reading and following the Primer. This will be done blindly at first. I also strognly suggest some reading to try to get at least the fundamentals under your belt.
And a water test is definitely a requirement. You must know where you are in order to determine how you are going to get to where you want to be.