Should we create the brand style guide before or after we design the touch-points (like stationery, marketing material, website, etc)? Why? Is there any rule on when it should be created? Thank you.
In my opinion that is not an isolated part of the job.
You can not create a visual guide if you have not experimented designing something, let us say the business card. Then this gives you a clue of some basic elements: complementary colors, aditional fonts, some use of space, elements, that can now be part of the guide.
Then you use this aditional elements and see how they react to let us say, a letter head. And so on.
So in reality they starts to build up together.
The purpose of the brand guide is to explain the design intent and possibly rationale to a wider audience so that they can replicate it. This happens when you have many people in the loop that have different needs.
Usually a bigger organization needs a guideline as there is a much wider need for collateral. In a smallish organization its pretty easy to numerate the kind of documents you need. Perhaps you need just stationery, brochure, a webpage and a e-mail footer, that's it. This can be easily done for you. But in a bigger company you might need, a dozen of poster templates, report templates, stationery for 20 departments, 30 webpages, 20 apps, marketing collateral (pens, boxes, usb drives, shirts, jackets, caps etc.), 5 different CAD drawing frames (electronics vs mechanical etc), product packaging, product design, laser etching templates, manuals, signs for your buildings, building maps, company cars and lorries, name plates... you name it. In addition you will be rolling many separate sub brands and marketing campaign regular intervals.
Thus, it is not possible for each and every design to be done by same person, or even one person to familiarize themselves with all that has been done. So to coordinate many designers to be coherent, and look like one entity you need some help. This is where brand guides start to kick in. The more diverse you are the better guides you need (which is why googles guide is so comprehensive, otherwise you would not recognize androids as android).
So you want one when you have many persons doing separate design activities and you feel like making your work more cohesive would make you more recognizable. Remember also that there are many different levels of brand guidelines, from light versions to very comprehensive. Sky is the limit, as is how much it costs you.