First, Apple has not made printing easy from your device. But there are ways around it. Hopefully this will get better in the future. 
 

Verify your device and printer are on the same wireless network.
All printing capability uses Wi-Fi. There is no direct connection to your printer or computer (unless using very specific third party applications, as mentioned later
on).

 
Check your device.
Not every device is capable of printing. The following devices are capable of
printing:
iPad2
iPad - iOS 4.2 or later
iPhone - 3GS or later
iPod Touch - 3rd Generation or later


Check your printer.
If your printer is AirPrint ready, you're done. See http://support.apple.com/kb/ht4356 for an updated list of AirPrint printers.

 
Other options.
If your device is print-ready, but not compatible with your printer, don't worry, you're in the same boat as most of us. But before you go out and buy another printer you do have some other options. There is third party software available on the web that you can download to help you print from your device. The software must be downloaded onto your MAC or PC-- there's nothing to install on your device. The way it works is that your computer acts as a middle man between your device and your printer. Keep in mind that your device, computer, and printer must all be on the same wireless network.



Once the software is installed on your computer,  make sure your computer is on and not in sleep mode. Check the software specifications to see what else you may have to do.  For example, I use Printopia on my MAC. I need to reconfigure Printopia when switching between photo and letter size paper. I use FingerPrint on my PC, but it's also designed to work with the MAC.

Printopia 
http://ecamm.com/mac/printopia/

FingerPrint 
http://www.collobos.com/

 
If you need to use a third party application, I highly recommend doing your homework and choosing one that works best for you. I have also heard that there are iTunes apps out there that can help with printing, but I've never tried them myself.


Visit Apple's site to view devices and printers that support AirPrint at http://support.apple.com/kb/ht4356.