A number of major retailers and furniture stores sell kids' furniture. Search via their websites or visit their store locations to find exactly what you are looking for. There are also a few companies dedicated exclusively to children's furniture.
Search websites of major furniture retailers and brands and, depending on your location, either find the store closest to you or order your products online. Companies that dedicate a section of their website to children's furniture in particular include Target, Ikea, Crate and Barrel, and Pottery Barn. These websites have kids' furniture organized either by category of furniture (beds, seating, storage, etc.), by age range (babies, children 3-7, children 8-12), or by collections of furniture that form a complete, coordinated child's bedroom.
Another option is to search through Amazon, eBay, or even Craigslist for less expensive furniture that is often used, including kids' furniture. Finally, ask family members, friends, and acquaintances who have older children or teenagers if they have kept their child's furniture. As children grow older, they outgrow beds, chairs, or even decor and toys, but these items might still be in near perfect condition.
Children's furniture is specifically designed with children's safety, entertainment, and rapidly growing size in mind, and can differ significantly from adult furniture.