DISCLAIMER: All programs that emulate an android system that allow you to play Summoners War without a physical device (tablet/phone) have been disabled by Com2uS. You can use app's to stream your device to your PC for recording or just playing from your computer.
For Android: Download Mobizen for your device and make an account. Choose a 4 number verification code. Download the program on your computer. You can connect screen via 3G, Wifi or USB but USB is by far the quickest. From here you can use a screen recording program or Livestream broadcasting program or just play Summoners War from your PC.
For iOS: Reflector 'app' is apparently the iOS equivalent to Mobizen. The Mobizen team are working on iOS support! Search for 'Reflector' for apple devices, it's a similar program. The latest firmware iOS Yosemite will feature support through Quicktime on PC that you can stream directly from the device with.