how do i authorize my computer to download my songs?

If the computer's running Mac OS X, move the cursor to the very top of the computer's screen, click on Store, and choose Authorize this Computer.

If the computer's running Windows, press the Alt and S keys and choose Authorize this Computer, or click here, follow the instructions, click on Store in the menu bar, and choose Authorize this Computer.

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Authorization

Macs: iTunes Store- About authorization and deauthorization.

Windows: How to Authorize or Deauthorize iTunes | PCWorld.

In iTunes you use the Authorize This Computer or De-authorize This Computer option under the Store menu in iTunes' menubar. For Windows use the ALT-S keys to access it. Or turn on Windows 7 and 8 iTunes menus: iTunes- Turning on iTunes menus in Windows 8 and 7.

Also see, iTunes Store- Authorize or deauthorize your Mac or PC