We watch Amazon videos and shows with our Prime membership.
There is a little device that hooks to the back of your TV called an Amazon Firestick. This is the connection between the TV and your Prime content.
It is a simple little device, small and plugs into the back of the TV into a USB port. You need a more modern TV with the USB port.
It requires a WIFI signal to operate, and you cannot download and store the movies. They have to be watched in real time. You can pause them, even shut them off and come back another day, but you cannot store them for offline use.
It's a great deal, I paid about 60 bucks for mine, one time purchase, no ongoing fees.