I would urge you to go to a salon and get it professionally done. Go to a good quality salon and ask for a consultation the week before. It should be free and they can give you an idea of what the process is going to be like.
If your hair is natural black you can use a box of blonde to lighten and then use a box of the shade of red you want. If you are a bottle black haired person you should purchase a stripper. Then a box of the red shade that you want.
Unfortunately your in for the long haul. In the end your hair will be quite damaged and you'll need hair therapy. Use a series or bleaches from strong to weak. You'll have to work the black out. But beware, red is also a very permanent color.
The simplest way to do this is to bleach your hair (also called stripping the color) and then re-color it to red. This can be very drying on your hair, however, and should be done with caution. Make sure you use conditioner!
to dye your hair from black to red you first have to lighten your hair with hair lightner then you have to dye your hair with a semi permanet hair color of your choice. I on not recommend doing this at home I would go to a proffessional.