As the previous poster suggested, the iPad can print directly and wirelessly to a WiFi printer that is AirPrint compatible. AirPrint is Apple's proprietary printing protocol that is currently supported by only a small number of printers. You can see the list here...
Apple - iPad - AirPrint
As another poster suggested, printers that are not AirPrint compatible can be used by means of a number of third-party apps. 'Print N Share' can print directly to most (but not all) wireless printers. I have yet to find a list of the supported printers. Print N Share can print to all printers via a wireless connection to a PC but, as you specifically mention you want to be able to print directly, you'll need to be careful if you go the Print N Share route. One advantage of Print N Share over some other third-party printing apps is that it cleverly inserts itself into the print menu of iPad apps that support printing and 'appears' to be an AirPrint printer.
As you're probably aware, not all iPad apps support in-app printing. So, for example, while Apple's 'Pages' (MS Word) app does support in-app AirPrint printing, its native calendar app does not.
If you do decide to go the Print N Share route you could search on this Forum for members who have used this app. The company used to market a similar (identical?) app called PrintCentral (I have this) until very recently and, for reasons that no one seems to know why, it's 'disappeared' from the app store. Print N Share seems to be identical in every respect. So it would be better to search the Forum, using the Search button near the top of the web page, for PrintCentral to find members' experiences with using this app.
Tim
Scotland