Form 1099-Q comes from the administrator or bank that manages your 529 plan or Coverdell ESA. If you set up the account and make contributions to it, then you are the owner and are the recipient of the 1099-Q. If you create one of the accounts to put someone other than yourself through school, that student has no control over the funds and is not responsible for any of the tax consequences.
The 1099-Q provides three key pieces of information. Box 1 reports your annual distributions or withdrawals from the account. The second box reports the portion of the distribution that represents the income or earnings of your initial investment. Finally, box 3 reports your basis in the distribution. Essentially, this is the amount of your distribution that relates to original contributions you make to the account.
The form also includes information on the type of account you own and amounts, if any, that you transfer between two qualified tuition plans.