How to root 2.3 ( Gingerbread ) Xperia™ Smartphones

 
  Go to settings > Security > Mark  "Unknown sources"

     Settings > Developer options > Mark USB debugging

     Settings > Xperia > connectivity > USB connection mode > select MSC mode

Rooting 4.0.2.A.0.42 and .58
Download this Rooting toolkit Link > 1 / 2 / 3 on your PC . Extract it, connect your phone to PC ( It should be on ) and wait for 2 minutes. After that run the rooting toolkit and root your phone.

Rooting 4.0.2.A.0.62

1. After marking the settings above, connect your phone to PC and wait for the adb drivers to be installed.
2. Download this rooting toolkit. Link >  1 /  2 / 3 /  4   and run it. It should now detect your phone and show an option to "root". Just click on it, wait till it finishes

If this doesn work then you'll have to flash a .42 firmware from this guide