What these adapters do is use your house's existing electrical wires to transmit data. Now, these adapters work fantastic if the house wiring is somewhat new, I've seen the adapters work in houses with 100 year old wiring, but the speeds do drop when the house wiring is older / in bad shape.
Then, after you have the powerline adapters, plugged in, plug one ethernet cable from your Verizon router into one of the adapters. From here, you can plug the other adapter into an outlet near the Roku, then run an ethernet cable directly to the Roku. If you really want wireless, you could purchase a wireless access point, but if the connection will just be for a Roku I strongly suggesting using a wired connection, as it will 98% of the time be more reliable.
I was about to say. If it's a Westell 6100 that's DSL. Extending that should be a piece of cake - go get a $30 Netgear Range Extender from a big box store and configure it.
For FiOS, if the router in use is a Westell 9100EM, I would suggest getting an upgrade to something newer from Verizon, and then use the FiOS Range Extender, which connects up to a standard Coaxial port in the house that is active for FiOS service. Wireless N's throughput improvement should help improve the performance even with a weaker signal.