Rideshare drivers are not required to go through any additional training when they are approved to drive for a rideshare company, though they do have to meet certain requirements. Some rideshare companies require a certain number of years of driving experience in addition to an age requirement to become a driver.
Rideshare companies carry insurance coverage to protect their drivers and their passengers, but drivers can elect to carry additional insurance coverage if they wish. If you are not at fault for the accident, then you should be covered by someones insurance, but rideshare accidents can get tricky when trying to determine liability. It is always important to consult with an attorney after you have been involved in a rideshare accident to make sure you protect your rights.