Not sure you mean when you say 'Free Support'.
I know Customer Support is free (when you call the manufacturer/company and ask for help and such).
However, I think you may be talking about Warranty.
Basically, a computer's warranty lasts for however long the agreement was (usually about 1 year). In short, within a year of purchase the computer can be repaired for free if it is damaged/non-functional. If something happens to the laptop after the 1-year warranty, you will need to pay to get it fixed.
Chances are that a used laptop won't have a valid warranty, but if it does, ask the guy for the documents.