I love these simple root solutions because it simply saves you time and heartache.
The software you need is pretty well named. Go to this page and download "Easy Root Tool for various Xperia devices" (EasyRootTool v12.1.zip at time of writing)
Plug your phone into the computer and make sure it detects properly. If needed, install the drivers (look at the screen on the phone) so the computer knows what device is connected.
Once that's all working, unplug the phone from your computer.
On the phone, activate "USB Debug Mode" from the Developer Options menu (To activate dev mode, go to Settings > About Phone > tap build number a few times)
Also on the phone, enable "Unknown sources" from the Security menu.
Unzip the contents of "EasyRootTool v12.1.zip".
- Run "install.bat"
- Plug in phone
- Look at the phone and confirm the "RSA key from computer" by ticking "Always allow from this computer" and pressing OK
- Let the script do it's thing
- Once it says "cleaning up", it's done. (I waited for a while there...)
- Open the Play Store and download SuperSU by Chainfire
- Run it and install it in normal mode (unless you know what you're doing)
- Reboot when prompted
- Enjoy, and consider donating to zxz0O0 on the XDA forums for all his hard work!
High-5's all round!