Most modern TVs do not have composite (red cable, with white and yellow audio cables).
They are not the same as component (red, green, and blue video cables).
I believe N64s only natively allow S-Video, composite, and coaxial (in order from best to worst).
See if your TV has any of those inputs, and get the appropriate cable. S-Video is best but not many TVs have it.
If not you'll either have to buy a new TV (CRT like Sony Trinitron, N64 looks vastly better on CRTs anyway), or else mod your N64 (e.g.
http://retrorgb.com/n64.html) or find some other third party solution like adapters.