FAQ: Corrective Color - From Black To Caramel Blond

I dyed my hair black about a year and a half ago. But I got tired of it and wanted to do something different. I wanted to let it grow out so I can cut off the black ends and have my natural hair color which is a dark brown. Then I would want to go lighter, like a caramel color with blonde highlights, but instead of waiting for my hair to grow out I stripped the black color off with "One n Only" I bought from Sally Beauty Supply. I used it twice but it didn't strip all of it off and my color was very uneven. At this point I decided to go to the salon today and the hairdresser said that I can't get it colored one solid light color but to get it higlighted and toned. She also said that my hair would be medium brown. I needed a change so I said OK. I hate my hair. I don't understand why she couldn't dye my hair a light color if she could highlight some parts. How could I lighten the darker parts of my hair from a dark brown to a lighter color at home?

Well this is quite a problem. I could almost say "a hairdressers nightmare". Let me take this whole issue step by step.
As I understand you colored your hair at home for year and a half. Now the application of your black color makes a big difference. That is HOW it should be applied, so if someone gets bored with color and needs a change it is stripped as easy as possible. Some people color over and over on already colored hair, which is WRONG. The proper application should be first time all over the hair and then when touch ups are needed only that re-growth gets colored, and if there is a little fading of the color that was tinted last time then that gets refreshed with diluted color which is left over from the application.
Now if the hair gets colored every time all over the hair (even the already colored hair) then anyone who wants to strip the tint has to deal with "over tinted hair". The pigment is build up to the point that it is hard to strip it well. The striping has to be done properly and all the hair needs to be saturated well so the "stripping" product works well. Then if needed do the stripping once more. Which you did, however I think that the stripping was either unevenly applied and/or the previous color applications were not applied well. If it would be you should have end up with  yellow hair after two "stripping" applications.
Now we are getting to the salon. I am not sure what you mean that your hair is medium brown. And you also didn't write what the colorist did to your hair. If she just highlighted your hair and left the rest of your hair be, that was not such a bad practice. If she did that she did it to protect your hair, so it doesn't all fall out.
You are asking a question: "why she couldn't dye my hair a light color if she could highlight some parts?" You can never color hair (which was previously tinted dark) with regular light color. You have to use a bleaching agent (on scalp bleach or stripper designed for stripping hair) to make it light.
So what your colorist would have to do is to bleach entire hair again as blond - perhaps to the yellow stage. She may have been scared what third application would do to your hair, since it is very strong chemical and if used improperly, or on week hair, or on damaged hair, the clients hair can go into the drain with the water. Than she would foil your hair for your highlights (that would be fourth application of bleach!) and in between the foil she would have to tone your hair with medium blond color, which would probably take darker due to the porosity of your hair. And again your blond hair color would probably wash out over time due to the porosity.
As to your last question "how could I lighten the darker parts of my hair from a dark brown to a lighter color at home?" I would say - I would not do it at home at this point. I would give my hair several conditioning treatments before I would go back to the salon for more highlights. Over time you will achieve the color you are looking for (always print an image found on internet of a model that has your hair type and that wears your desired color/style/cut), but until then you have to be patient. When going from a very dark tinted hair to a blond shade it always takes several sessions. Unfortunately.

This post should be taken as a first step for a discussion with your hairdresser and/or colorist about your ideas, desires or problems with your hair. Under no circumstances, you should act upon this post ONLY. I strongly advice you to have your hair done by a skilled and reputable hairdresser/colorist in your area.