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I’ve never rooted that particular device, but it will be a two step process. You have to unlock the bootloader to gain root access, so first you will need to unlock the bootloader. Sony actually provides an overview and basic on how to do this. http://unlockbootloader.sonymobile.com/
Here is a step by step guide for unlocking the bootloader: https://sites.google.com/site/projectfreexperia/download/bootloader-unlo...
Assuming you sucessfully unlock the bootloader, you will need to flash a custom ROM to gain root access on your device. I suggest looking at one of the Cyanogen ROMs to start out. The FreeExperia Project on xda developers should give you some guidance on this step. You might also want to check out some of the forums on Android Central or Android Authority that are specifically devoted to you device, since those people have actual experience with it. It can sound really complex at first, but if you look through the steps and carefully follow them, only proceeding when you are sure you understand each step, you will be fine. Of course, there is always a chance that you will brick your device, but if you take your time, that is pretty unlikely.