How do you install your own DIY radon mitigation system?

Removing radon gas with sub-slab suction is not something we would call ‘easy’; and our first recommendation would be to have it done by a pro, especially given the questions you mention above. I assume you’ve had your air tested and it showed high levels of radon? Here by the way are all our page all about mitigation – 

Testing for radon gas in homes  and radon mitigation techniques for basements and crawlspaces

Sub-slab depressurization is a great method for radon removal, but if the basement is not finished space, one mitigation strategy is installing a dedicated HRV in the basement that is activated by a radon gas detector; that would eliminate the risk of accidentally damaging any pipes below the slab since you don’t know where they are. The HRV can be set to leave the basement pressurized to keep the radon gas down. That may be a risk-free way to deal with radon (depending on how severe it is), and provide heat recovery and fresh air at the same time. That puts the job in the hands of an HVAC installer. 

If you do plan to undertake a sub-slab removal technique, unfortunately you are the only one that can answer your own questions regarding what lies beneath the slab and best location for drilling. I would first ask you a few questions – is there radiant infloor heat? That would significantly raise the stakes of a DIY project. And if you did test the air already, how high was the reading? Is it finished living space? Is the garage on the same level of the basement or is it a slab on grade? Sorry for al the questions, radon gas in homes is serious business and we want to be sure to provide the right assistance.