Corporations and limited liability companies (LLCs) are legal people. This means that you can sue, and enforce a judgment against, the business entity itself. You should not sue the owners, officers, or managers of the corporation or LLC as individuals, unless you have a personal claim against them that is separate from their role in the corporation or LLC. That's because in most situations, the real people who own or operate the corporation or LLC aren't themselves legally liable to pay the corporation's or LLC's debts (unless there was fraud or a personal guaranty). This concept is called personal limited liability and is a big reason many people choose to incorporate or form an LLC in the first place.
Be sure to list the full name of the corporation or LLC when you file suit (John's Liquors, Inc., a Corporation, or John's Liquors, LLC). Here again, the name on the door or on the stationery may not be the organization's real name, as corporations and LLCs sometimes use fictitious names. To be sure, check with the city or county business license office where the corporation or LLC is headquartered. Information is also usually available from either the secretary of state or the corporations commissioner's office for your state.
You may sue a corporation or LLC in your state if it does business there, even if its headquarters are in another state.