Upgrade OS X Server Lion 10.7.5

We have Mac mini with below specifications:

Mac mini Server
Processor 2 GHz Intel Core i7
Memory 8 GB 1333 MHz DDR3
Graphics Intel HD Graphics 3000 512 MB
Software Mac OS X Server Lion 10.7.5 (11G63)

We want to upgrade Xcode 4.6 version to 5.0.1 to work with iOS 7 SDK. We are 5-6 people use this Mac mini for iOS development.

We know that Xcode 5.0.1 is compatible with OS X 10.8.4 or later.
Can you please send me instructions/way to install/upgrade our current Mac OS X Server Lion 10.7.5 to Mac OS X Server Lion 10.8.4 or later?

Firstly find out if a straight upgrade to Mavericks server will meet your needs, you can download and upgrade from the Apple store

If you want 10.8 server, and its not listed on the Apple store, then give Apple a call, I know they were still selling the previous version of server when I called earlier in the year.

They should give you a link on the store to purchase OSX Server 10.8. Its then just a download and upgrade over your existing 10.7 server

Make sure you backup, or even better clone the disk of your old server before the upgrade, just in case. But the upgrade should be fine