Foreword: backup, backup, backup. Before starting the upgrade process you should make a backup of your site and DB so that, in case the procedure fails, you'll be able to restore your site to a working condition.
You should also make sure that all the extensions are available to you in Joomla 3.x compatible format.
Upgrade Joomla to 3.x
This procedure is the recommended standard procedure to upgrade your Joomla installation. If any problem arise or to get more information please refer to official Joomla documentation and to the Joomla Forum.
1) Login to the backend
2) Extensions > Extension Manager > Update
3) Click Purge Cache
4) Components > Joomla Update
5) Click Options button
6) Select 'Short term support' as update server
7) You should see the latest version of Joomla 3.x
8) Click 'Install the update'
Upgrade Custom Properties to version 3
1) Extensions > Exetnsion manager > Install
2) Upload and Install Custom Properties installer package
Finalise Custom Properties upgrade
At this stage Custom Properties 3 is already installed, CP fields are there and the tags are still correctly assigned, but most of localized strings (i.e. menu, parameters, etc) are displayed incorrectly. Two operations need to be carried out manually.
1) delete the old language files, because CP 3 have them stored in a different place and the old one interferes. The files are:
2) Review and Save Custom Properties configuration: Components > Custom Properties
3) Click Options
Update Custom Properties Menu Items (if required)
Old Custom Properties menu items don't work under Joomla 3.x. You have to edit them, re-select Custom Properties menu item type and set other parameters as required.