You have three main options for printing from your iPhone to Canon printer. If you have a compatible model you can use Apple's own AirPrint tool or Canon's own application. If you have another printer model you can use a third-party application.
Check your printer documentation to see if it has the PIXMA or SELPHY branding Only these Canon models work with the Canon app method
Download and install the Canon iEPP app from the iTunes App Store.
Open the app and follow the on-screen instructions. You can choose Photo Albums to print a picture you have already taken, or Camera to take a new picture and have it print out immediately. Once the app is installed, you'll also get a new "Print" option in any other app that allows you to view PDF documents. These are the only three situations in which you can print from the iPhone using the Canon app.
Check you have a compatible Canon printer by looking through Apple's current list (see Resources.) Around 100 Canon models are compatible. These include many models with numbers starting "IP", "MG", "MX" and "PRO."
Check that your printer is switched on and that it is connected to the same network (wireless or wired) as your iPhone.
Tap the action icon in the app from which you want to print. This icon looks like an arrow coming out of a box and pointing to the right. Then tap Print.
Select your printer and choose any relevant print options in prompted, then tap Print again.
You may need to update your firmware at Canon's website (see Resources) before your printer will work with AirPrint.
If you don't have a compatible model, you may be able to use a third-party iPhone application. Examples (see Resources) include Print n Share by EuroSmartz, PrinterShare by Dynamix and ePrint by Microtech. Depending on your chosen app and printer model, you may be able to print directly through a wireless network, or may have to install software on your computer and make sure the computer is switched on when you print.
Check reviews and support documentation before buying an app as exactly what types of file or document you can print may vary.