To feed your sidekicks, first you have to complete the sidekick tutorials in the Hub World. From the main menu select Toy Box and then Toy Box Hub.
Once the Hub World has loaded, go talk to Woody from Toy Story (the cowboy) as he's the sidekick tutor. Follow along with the tutorial until you get to the farm, learn how to plant, and learn how to feed your sidekick. Once you can feed your sidekick, you can exit the Hub World.
The easiest way to get food to feed your sidekicks is from community maps. From the main menu select Community Content -> Disney's Toy Boxes -> press Start (three lines) to search and look for "farm" without quotes and select Go. There's a few farm maps that are good ("FARM RACE" and "Super Rare Farm" are popular). The best one is probably "Infinity Farm." This map lets you go through different doors to farm the foods that increase particular stats. Just farm up 50 items, feed them to a sidekick, and achievement unlocked.
Also, feel free to download the map so you can play it offline. Don't save the map either so everything will grow back next time you load. But you'll still keep all your stats and items.