General information
Every compound will have different procedures regarding utilities costs and how to pay them.
Some compounds will have cheaper electricity costs after a certain hour, some compounds charge electricity, water and gas on a monthly basis whilst some other compounds may be bi-monthly or maybe even every 3rd month.
Whatever your payment schedule or cost may be, the method of payment for these utilities remains mostly the same with these options available:
Generally you will always receive a utilities payment slip in your mailbox within the first week of the month in which you have to pay your fees. Your landlord generally will be able to tell you how frequent this will be.
Your utilities bill generally will be something similar to this:

Whilst it may seem confusing at first, you generally simply need to check the numerical numbers on the sheet to make sense of it. The first thing you want to check is whether the address is correct, to make sure it is your bill, as sometimes they get mixed up in the mailbox, whilst you can generally ignore the name it is addressed to as this will be generally your landlord's. The next thing you want to check is on the right side numerical numbers which is the amount you owe. Sometimes this number may seem big, but you should be aware for how many months your paying for. An electricity bill for three months will obviously be larger than one for a single month.

How to pay?
Offline:
You can simply take this bill to most local convenience stores such as Seven-Eleven, FamilyMart and Haode. Furthermore post offices and banks will also take your bill, however this may not be as as convenient as the 24-hour convienence stores, banks and post offices generally will have a line. Wherever you take it to, they will scan the bar code, then you pay the proposed amount and then they will stamp the bill and give it back to you. You should keep your receipt, at least till your next payment in case you need to proof your payment.

Online:
You may also pay your bill online. Most of the bills will have a numerical account number on the top that is unique to you. Entering this number into the application Alipay allows you to select auto-payment of your bills so that you will never forget them or you can manually pay them whenever they are due. They do not remind you that you have to pay them if you do not select the auto payment, so it may be prudent to check your mailbox so that you do not forget, as they will still continue sending you the paper bill whether you pay online or not.

More on Alipay: Alipay is an online payment system similar to Paypal / Applepay. Here is the link to our article on how to set up Alipay. It is available in English and once set up it is fairly straightforward to use, especially when used for paying your utilities bills. It has various other uses as well such as transferring money, payment at accepted stores such as restaurants and convenience stores, paying for your Taobao shopping, movie tickets and topping up your mobile just to name a few.

What if you miss a payment?
Offline:
If you pay using the mail they send you, all the bar codes printed there have an expiration date. That means that if you go on a holiday and come back on a month where you have to pay your bills, you may not be able to use this bar code in convenience stores, banks or post offices. Instead if you continue to insist to pay in cash using the mail, you must go to their branch offices. Every area has a branch office and you can ask your landlord to find out where yours is. Once you reach the branch office payment is very much the same as in convenience stores, post offices and banks. If you miss more than one payment you may find that they have cut you off and it will take generally a day to restore the service to you.

Online:
If you pay online, and you miss one payment you can still continue pay it as long as the option is available, which generally is for a few months. Once it is not available anymore you must go to the local branch and you can pay using your account number or by stating your address.

Pro Tip:
When you move to a new apartment always make sure that the previous tenant has paid off his or her fees. Generally the first month when you receive your bills make sure that you check the dates of the bill, and if it included months where you have not lived in the apartment make sure the landlord acknowledges it and helps you partially cover it.

Useful Chinese keywords:
水电煤 - ShuiDianMei – Lit. Water, Electricty, Gas, Chinese will use this to describe utilities
账号 - Zhanghao - Account/Account number
支付宝 - ZhiFuBao - Alipay