There are several methods for paying bills in Paraguay.
You can either pay directly at each of the service providers (ANDE, Essap, Copaco, etc). However, more convenient payment methods are available such as bill payment stores such as Aqui Pago or Pago Express with locations all accross the country where you can pay almost any type of bills including electric, water, cel phone, tuition, etc. You may also opt for automatic debit through your credit or debit card (you can request this at any paraguayan bank that issues the card). Another convenient method is to pay online through a company called Pago Movil Infonet (infonet.com.py) where you simply register for free and select the bills you want to pay using credit card or other means.