Hooking up an NES system to a modern TV is a very simple process, for the most part. However, if you have managed to obtain a rare, and quite popular, top-loading model, it can be slightly more confusing.
Plug the RCA cables into their corresponding-coloured jacks on the side of the NES. One will be a "video out" and the other will be a "sound out."
Plug the other end of the RCA cable into the corresponding jacks on your TV. Note that most TVs have two audio inputs. One will remain unused.
Set your TV channel to "aux" or "input" and power up your NES. The game image should be visible.
Unplug antenna/cable/VCR or anything else that may be plugged into the antenna socket on the TV.
Plug the antenna/cable/VCR into the corresponding socket on the RF adaptor. Plug the RF adaptors output into the antenna input on the TV
Plug the RF adaptor into the RF out socket on the back of the NES system. Set the RF adaptor to channel 3.
Turn your TV on and change the channel to channel 3 and turn on your NES. Your game image should be visible.
Plug the NES coaxle output into the coaxle input of an old VCR.
Plug and RCA cable into the RCA outputs on the VCR.
Plug the RCA cable into the corresponding inputs on the TV and turn the TV to its "input" or "auxiliary" channel. Your game image should be visible.
If you have the top-loading style NES and no VHS, you can use any sort of DVD player with a coax input or buy any number of coax-to-RCA converters from any local electronics store.