For me, the shop sponsorship means I am going to my LBS to buy stuff when I need it and not going online. The prices generally are pretty competitive, as is the ordering time.

Sometimes my LBS is cheaper than online. Sometimes online is cheaper. The sponsor shops margins are reduced by my business, but, my sponsor shops knows they have my business and knows I'll send business there. Also, on the rare occasion I can't fix something, I bring it to them, and they generally turn my bike around quickly.

As for finding a sponsored club/team, there is a list on USAC's website: Clubs - USA Cycling

Find a local one and look them up. Some clubs are limited to only cat 1s and 2s. Some clubs have strict membership requirements or invite new members. Some clubs are open to anyone who wants to join.