dyeing your hair
Is lots of fun and only a really platinum blonde tends to damage it. Yes you can get different coloured hair at the same time (highlights). The stylish will have to separate the areas you want in a different colour with elastic bands or foil or some such thing. Or she may colour your whole head and go over certain areas with additional colour. If that's the case expect the initial highlighted area to change colours in a few days (or sometimes hours).
Absolutely DO NOT colour your own hair if you want more than one colour. You will turn it some ghastly colour that you absolutely hate and then you'll have to go to a salon and get it corrected and then probably have it re-dyed which will cost a pretty penny.
If you go to a professional first time around you will probably get great results and it is smart to go to a salon someone else has recommended.