You cannot terminate service online. You must call in to CS or stop by a Verizon corporate store.
What do you intend to do with your number? Are you switching providers? If so, you wouldn't want to initiate the termination with Verizon. You would go to the new provider and ask to have your number ported over to the new provider. When the port is complete, your service will automatically be terminated with Verizon.
If you simply want to terminate service and call or stop by to do so, the service will stop at the time you initiate the termination. I don't think you can ask to have it "scheduled" to be terminated at a later date, but you could always ask. Additionally, Verizon does NOT pro-rate service for your last month so you WILL NOT get a refund of any service for which you have already paid. With this in mind, you should plan to terminate the service close to the end of your billing cycle.