Just a few quick definitions of amelioration and mitigation:

I'll start with mitigation as it is probably the term that most people are aware of. Steffan et al (2007) describe mitigation as:
"taking pressure off the Earth system through drastically improved technology and management, wise use of Earth's resources, control of human and domestic animal population, and overall careful use and restoration of the natural environment." This can be done through a wide variety of things such as publicly known renewable energy sources (wind, solar, tidal etc) to wholesale changes in building design and manufacture. 

The amelioration efforts are likened by Vaughan and Lenton (2011) to medicating a sick patient, deliberately treating the climate to decrease levels of atmospheric CO2, this is done through geoengineering techniques which are branched into solar radiation management (SRM) and carbon dioxide removal (CDR).

I'll detail the techniques in later blogs but for now that's it,

Cheers,
Sam.