How to buy tickets and take the Guangzhou metro

Guangzhou has a very extensive metro network of subway trains that connects all transportation hubs (like airport and various train stations) together as well as most of the major points of interest in the city
It's the cheapest way to get around the city, and during rush hours of 7-9am and 4-7pm, it's also the fastest way to get to pretty much anywhere in the city
Guangzhou metro map:You can check out the official website for the latest system map
Fares:
The minimum fare is ¥2 RMB ($0.3USD), and goes up by distance
Most of your rides will not be more than ¥4RMB ($0.6USD), and going from one end of the city to the other will only cost you ¥8RMB ($1.1USD)
How to buy tickets: most visitors buy the single-journey ticket because it's the easiest one to get. The reloadable cards is more for longer-term residents

You can buy the single-journey tickets at the automated machines at the entrance of each station:Pay attention to the scrolling electronic text displayed at the top of these machines, as they tell you if that particular machine accepts cash or only mobile pay (WeChat Pay and AliPay). The ones that only accepts mobile pay will say "Only WeChat Pay and AliPay". The ones that accept cash will say "notes accepted" (like the left-most machine in the picture above)
Go to the machine, and switch it to English
Then you will need to select your destination station. First click on the metro line number of your destination station, which will bring up a list of all the stations on that line
Then click on name of your destination station:
Then click on the number of tickets you need. 1 is selected by default:
Then insert the ¥1 coins or ¥5 and ¥10 bank notes into the slots at the top right of the machines. Only these three denominations are accepted
Then voila your ticket, which is a plastic token, will be dispensed at bottom of the machine. Any change due will also be dispensed here as well

How to buy tickets using WeChat Pay or AliPay: if you have set up WeChat Pay or AliPay (which you can now as a foreigner since November 2019), you can use these apps to pay for your ticket instead of using cash

On the same screen as where you select the number of tickets (after step 5 above), you just need to click on the button for either AliPay or WeChat Pay:
Clicking on it will bring up the payments QR code:
Scan the QR code with your AliPay or WeChat Pay app, and then authorize the payment in your app. Your ticket will be dispensed almost instantaneously. That's it

Once you have your ticket (the plastic token), walk over to the turnstile to get into the station. Here, tap your token like this:The only exception is the APM line, which has a flat fare no matter the distance. Here you insert your token (instead of tapping) to get into the station
You must hold on to your token the entire ride. When you get to your destination station, at the exit, insert your token into the turnstile to get out, like this:

Which planning apps to use: Baidu Maps (and the iOS app and the Android app) is probably the best tool available to help you plan out how to use the metro to get to your final destination, but unfortunately it's only available in Chinese. Google Maps is pretty useless when it comes to public transportation information in China. Another useful app is MetroMan, which will show which subway lines to take, but you to tell the app what's the starting and ending stations
Metro hours:
All lines start operating at 6am in the morning
Most lines stop operating by around 11:30pm
The specific stop times vary by line and I think a few lines go as late as midnight. Check the official website for the line-by-line details

Let me add an updated version of this brief