There are lots of 'how to get switchable graphics to work' guides but I found none on how to configure a system for switchable graphics operation on Ubuntu from the ground up, nor explaining the current driver situation for particular computer models (integrated+discrete combinations). Example: https://help.ubuntu.com/community/HybridGraphics

My system being mature and on Intel integrated card also makes things complicated.

System information:
Ubuntu 12.04 amd64, installed clean with system configured to use only the integrated Intel card Lenovo Thinkpad T500
Intel GMA 4500MHD / ATI Mobility Radeon HD 3650

Current situation:
Mature and up-to-date system with no configuration changes to what's given above.
I've made a backup image of the system (Clonezilla) so regardless of what's written below let's assume it's our starting point. If something in What I have already tried is not clear you may as well diregard it.

What I have already tried:
Configuring BIOS to switchable graphics and:

1. Installing Additional Hardware drivers - returned an error.
2. Installing proprietary amd-driver-installer-12.6-legacy-x86.x86_64.run automatically - system starts to 'low-graphics mode'.
3. Tried fixing as per https://help.ubuntu.com/community/BinaryDriverHowto/ATI#Manually_installing_Catalyst_12.6.2C_special_case_for_Intel.2BAC8-ATI_hybrid_graphics
4. Got lost, gave up.

Please note that while configuring BIOS for integrated graphics only is pretty straightforward, configuring for switchable graphics is not.