How to update Sony Xperia C smart phone with Lollipop Android OS?

Sorry, but Sony Xperia C does not support Lollipop update. It is not possible to upgrade it to the Android Lollipop OS. You can refer to the below link for more information.

The above procedure Involves rooting your device which will void your warranty. It also carries a likelihood of bricking your phone if you miss a single step.
A custom ROM is based on the official Android OS , but it will not be as same as the official version. No matter how meticulously it has been made, it always remains a third party development. The author of the above response seems to have missed giving info about this point, hence this clarification.
If you are talking about about the official Lollipop version for your device, sorry to say that the it will not get the official Lollipop update.