Computer Networking Wireless (Routers)?

Ok guys I have a wireless G router kinda outdated but it does the job for now, My question is can you add another router to a network that I have set up, without a Ethernet cable from the wired router to the new router and have it pick up a signal from the router that is hard wired to my computer? What I am trying to establish is I want to be able to access my direct tv multi room viewing but it needs internet connection. I'd like to get another router that can pick up a signal from the existing router "without wires" and then use an Ethernet cable from the new router to the back of the dvr? is this possible? and what kinda router/hardware would I need? my computer router is in my office and my dvr is downstairs.