Printing from your iDevice has been made particularly easy, provided you are using a printer that supports AirPrint. If your printer is supported, all you have to do is click the action icon (shown below) on the page that you want to print and select the Print option.
Simply choose your AirPrint compatible printer (which must be connected to the same network as your iDevice), choose your settings and hit Print.
AirPrint is available from many places, such as Photos, Safari, Mail etc. It may also be available in apps that you download from the App Store. For more information and a list of compatible printers, you can view this article from Apple's website which lists compatible printers by manufacturer.
As many older printers are not AirPrint compatible, there are also some other ways to print. For example, if you are using a HP printer, have a look at the HP ePrint app from the App Store. This will allow you to print to many more HP printers, directly from your iDevice. To do so, you must use the HP ePrint App, not the action button above, to print. The HP ePrint app is quite clever. It can access your photo library and you can also load documents directly into the ePrint app to print them. I've used it with my HP OfficeJet 4500 to print photos and it works a treat!