I have absolutely no idea how people start consulting. How old are they? Did they work something else before? Did they major in anything? Are they all independent or work at consulting companies?
OK, the point is any of these things could be the case, or not. Some people start consulting immediately. Some don't start until they have been working "regular jobs" for 20 years. Some start young, some start old, etc. There is no one way to start. Just start.
There's only one consistent answer to any questions WRT consulting and that is "it depends."
I've been in your shoes before, trying to figure out exactly what consultants do and how to start doing it. Once I gave up on finding a simple answer and just did it I started to understand the game.
Read the book Million Dollar Consulting. It pretty much gives a step-by-step guide, from lead gen to writing proposals to how to bill by value:
http://www.amazon.com/s/ref=nb_sb_ss_c_0_19?url=search-alias...
It repeats itself a lot and is generally poorly written, but there's still a reason why it's been the top consulting book for decades.