You only get paid for completing rides. Having the app open does nothing. How much you receive per ride varies greatly depending on location and time of day. Typically there is a base fee for the ride plus a per mile or per minute rate and some other potential fees. Uber then adds a 25% commission that they keep.
Minimum wage would come into play if a driver complete x hours of driving but the average hourly rate over those hours falls below the state’s minimum wage. In those situations it would be Uber’s responsibility to make up that difference. This is similar to to how restaurant servers in the US are paid. Most of the time their tips far exceed the minimum wage when averaged over their whole shift. In the occasional cases where tips are terrible or business is slow the restaurant is responsible for making up that difference to meet minimum wage requirements. These “tech” companies are stating they shouldn’t be responsible for that because they don’t have employees, just contractors who use their app.