Information about how to use Uber is, unsurprisingly, available on their website:
https://www.uber.com/en-GB/blog/how-to-use-uber-for-the-first-time/
Possibly the key thing to note there is the bit about 'dynamic pricing', which follows the airline model for setting fares, whereby fares are lower when there's little demand but higher when everyone wants to travel at once. There's no nasty surprise at the end of your journey though, as you're quoted the fare on the app before you commit to making a booking.
All Uber drivers hold Private Hire licences and, as such, are subject to the same background checks as any other Private Hire or Hackney Carriage licence holder is. e.g. here's the procedure in Birmingham:
https://www.uber.com/gb/en/drive/birmingham/get-a-license/