I would like to find out how to safely change my haircolor given the
fact that it is already colored and I have naturally black hair.

Background: I have naturally black hair. About a week ago, I tried to
dye it with Clairol's Hydrence product (shade #36) to light Brown.
Unfortunately, it came out more redish than brown, and I am quite
disatisfied. I want to find out a step-by-step (including specific
brands, shades, etc.) to achieving a "dirty blonde" or very dark
blonde look on my already colored hair, even if it involves some kind
of bleaching.

I'm looking for a solution soon as I do not care for the way my hair
looks now. The hair is short and not damaged.

I strongly recommend that you let a professional hair colorist do this
for you. Going from black to blonde is a multi-step procedure; if it
is not done properly, you may end up with an ugly shade of orange, and
your hair can be damaged. Since you've already used a coloring
product, the situation is even trickier than it would have been on
"virgin hair."

There's some good advice here:

http://www.isnow.com/hair/features/0903moltaji2.html