I would say the best place to start is getting dressage tuition, as you mentioned. Although lessons can sometimes burn a hole in your pocket, they really are essential if you want to take up a sport professionally one day. Look around your area and find out what instructors are available. If you have more then one in your area, try out a few and see which teaching style suits you :)
Once you have a dressage instructor, the possibilities are endless :) You should be comfortable enough with your coach to be able to discuss anything/everything horse related, including your aspirations to become a professional dressage rider!
Also, just remember, your first horse should teach you alot, but don't expect him/her to take you to the top :) So if things don't go exactly according to plan, don't give up hope!
And last of all, dream big, but keep goals realistic and you will go a long way