Turning off voicemail usually involves going through the voicemail settings on the user's account. The exact method depends on the service provider. In the case of smartphones, the voicemail feature might be controlled on the phone.
Some people might find calling the phone company the easiest method for turning off voicemail service. If the voicemail service is a paid feature and the user does not want the service, calling the provider to cancel the service is usually the only way that the voicemail service can be turned off. By canceling the service, the user won't have to pay for a service they are not using.