I don't think it's very possible. Even young college graduates with degrees enter the work force at relatively low salaries. Low salaries, plus cost of living and cost of starting off on your own usually don't allow someone to save 10-15K a year.
A Canadian example: Here in Canada, the average starting salary for a university grad is between 30-40K. And if you choose a trade (like carpentry, electrician etc.) you still must apprentice on the job for years before you begin generating decent enough income to save the amounts you're talking about. So let's say 35 for the example:
Income tax off the bat will bring you down to about to about 23K. Let's say you have cheap rent at about 600$/month, that leaves you with less than 16K. You have to eat, pay your utilities, (heat, phone, insurance etc.) not to mention transportation (car, or public) clothes, home supplies, probably some entertainment expenses - and of course a computer and internet service. It certainly doesn't leave you with much. And you DON'T have a degree, you're probably starting lower than this example. So whoever told you that it's possible to save 10-15K a year by NOT going to school has probably never tried (or is living at home with Mom & Dad paying all the bills - that's not saving, that's being a dependant)