Printing from your phone or tablet has gotten a lot easier in the last few years. Most printers now support mobile printing out of the box, and you don't need any special hardware to make it work. Just your printer, your mobile device, and a Wi-Fi connection.
The simplest method is the printer's mobile app, which is free on both iOS and Android. Download it, open it, and the app will search for printers on your network. Once it finds yours, tap on it and you're connected. From there you can print photos, documents, PDFs, and web pages directly from your phone.
If you're on an iPhone or iPad, AirPrint works without any app at all. As long as your printer supports AirPrint and it's on the same Wi-Fi network as your device, you can print from any app that has a print option. Open a document, tap Share, tap Print, select your printer, and go. It really is that easy.
Android users have Google Cloud Print's successor built into the OS through the default print service. Go to your phone's settings, find Printing under Connected Devices, and your printer should show up if it's network-connected. You can also use Wi-Fi Direct for a direct connection between your phone and the printer without needing a router in between.
One thing to know. Mobile print jobs default to standard quality and single-sided printing. If you want duplex or higher resolution, you'll usually need to change those settings in the print dialog before hitting print. The printer's mobile app gives you more control over these options than the built-in system print dialog does.