My hair is naturally black and I want to make my hair a brown with blonde highlights and little reddish strands... like this picture...

http://www.mybellacolor.com/BROWN_MULTI_COLORED_HAIR_SWATCH.jpg

I want my friend to do the hair coloring because she has gone to beauty school... but just for future reference how can I try to do this myself if at all possible?

Sweetie, if your hair is naturally black, it will be hard for you to maintain your desired color and highlights by yourself. To go from black hair to brown, you will need to pre-lighten your hair and then deposit the selected all over color. You can also use a high-lift color hair to achieve results. Then wait 1 or 2 weeks and do the highlights. Since your friend has some experience in hair coloring, hopefully, he/she will be able to achieve your desired color and help you maintain the results.