Please consider the following steps to update ArcGIS Desktop, ArcGIS Server and ArcGIS Engine.
Note: In order to get the latest Esri patches also have a look at http://support.esri.com/en/downloads/patches-servicepacks/.
Note: Find more information about upgrading you ArcGIS products in the Esri installation guide.
Download Esri patch finder
Please use the Esri patch finder tool from the link above to check your current installed versions of Esri patches.

Download Esri patch finder
Download Esri patches
Compare the result of the patch finder tool with the patches provided from Esri, download the missing patches and install them on your system.
Note: Use the filter function to find the latest patches of an Esri component.

Filter function for searching Esri patches
Installation of an ArcGIS Desktop Patch
Note: Use the Esri Patch Finder Tool to check whether all installed ArcGIS products (desktop, server, engine,...) have the same available patches installed. If a request for reboot appears during the installation of the patches, this must be done. The reboot can also take place at the end of the installation of all patches.