how to use wireless printer with time machine???

Hello lifespan of iMac,

It sounds like you are using the Time Capsule with Time Machine and want to connect a printer to the Time Capsule.

Here is a great article for troubleshooting a USB connected printer with your Time Capsule:

USB printer troubleshooting for AirPort Express, AirPort Extreme, and AirPort Time Capsule

http://support.apple.com/kb/TS1253.

Symptoms

Your USB printer may work the way you expected it to when connected to your computer, but not when it's connected to your AirPort Express, AirPort Extreme or AirPort Time Capsule for printer sharing.

Note: AirPort Express, AirPort Extreme and AirPort Time Capsule printer sharing is for printing only, not for printer utilities or other special features that may require a direct USB connection.

Resolution

Check for software updates

Be sure that you have the most recent OS X or iOS software updates, and the latest firmware for your AirPortproduct before trying to print.

Note: Printing via an iOS device requires an AirPrint enabled printer. Refer to AirPrint Basics for a list of AirPrint enabled printers.

Disconnect and reconnect

1. Disconnect the AirPort Express, AirPort Extreme or AirPort Time Capsule from a power outlet.
2. Turn off the printer.
3. Be sure the USB cable from the printer is connected to the AirPort Express, AirPort Extreme or AirPort Time Capsule.
4. Turn on the printer.
5. Reconnect the AirPort Express, AirPort Extreme or AirPort Time Capsule to a power outlet and wait for it to become ready.
6. Try to print.

Check your printer driver

Check the website of the printer's manufacturer for the latest driver version.

Reset Printing System

Use these steps on your Mac if the above steps do not help.

1. Open System Preferences > Print & Fax preferences.
2. Control-click or right-click in the Printers section on the left.
3. Choose Reset printing system....
4. Click OK.
5. Click the + button to add your printer again.
6. Try to print.

Still not working?

If your printer still doesn't work with AirPort Express, AirPort Extreme or AirPort Time Capsule printer sharing, but does work when directly connected to your Mac, contact the printer manufacturer for additional information and to verify that printer sharing is supported.

Additional Information

Refer to this article for additional help setting up a USB printer on your Wi-Fi network.

Refer to AirPrint Setup and Troubleshooting for additional AirPrint help for your iPhone or iPad.

All the very best,

Sterling