Anyone know a common website people use for builds and is it trustworthy for gameplay?
The most popular and most generally accepted by the community is SoloMid.net. The reason for this strong community acceptance is its Approved/Featured Guides system - guides are submitted by community members (including professional players), and from there, they are Approved by site administrators if found to be of good quality, and Featured if found to be of particularly good quality or are written by a professional player renowned for their expertise in that role or champion.
There are less popular/less rigorously vetted sites such as LoLPro and Mobafire, but their content is not considered to be as "definitive" as SoloMid's. Most veteran players will suggest SoloMid as a resource, due to the heavy influence from professional League players.
Most used website for builds and champion info is mobafire.
Best LoL sites:
LoLDB Great site known for its in depth statistics, though not as good as Solomid for guides
Mobafire (Best site for countless builds for each champion as well as champion info)
League of Legends wiki (Contains champion info,info for every patch,and everything else LoL related,but does not contain builds)
Leaguecraft (contains custom skins,champion info and guides for each champion)