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Guns are dangerous. Customers are unpredictable. Logically, it follows that customers with guns are unpredictable and dangerous. Because of this common sense logic, many business owners simply don't want customers or employees or anyone bringing guns into their businesses.
In every state, business owners can legally prohibit both customers and employees from bringing guns into their businesses (although some states make an exception that allows employees to bring guns to work so long as the gun remains locked in their vehicle in the parking lot).
First and foremost, for business owners that want to prohibit guns in the workplace or in their business, using common sense when enforcing the policy is a must. People with guns can kill, and exercising discretion when it comes to telling an armed individual to leave your store is the most important thing you can do.
If the person is clearly agitated, approaching the person with caution, or perhaps calling security, or the police, might be advisable to attempting to diffuse the situation yourself. However, do not hesitate to call the police if the individual refuses to leave after an initial request. Whether or not you want to warn the individual about your call to the police is discretionary, but generally, be aware that threatening to call the police or warning that the police have been called can escalate a tense situation.
In many states, including the notorious pro-gun state of Texas, businesses can prohibit customers from carrying guns into their stores by placing signs at the entrances. Even individuals with concealed carry permits can be prohibited from carrying their gun, concealed or not, into a business.
However, be forewarned: for signage to be legal, in many states it must conform to the state's requirements. For instance, in Texas, the signs must have lettering that is at least one inch tall. If your state allows you to prohibit guns via a sign, you may be able to call the police if you spot a gun-carrying customer and not bother with even confronting the customer.
Regardless of whether your state requires clears signage to prohibit guns, having clear signs that inform customers of your policy is simply good business. Most gun owners are rational individuals who understand that a business has a compelling reason behind banning guns, and will be even more understanding if that policy is clearly posted for everyone to see and follow.