JS newbie confuse about common test procedure

All:

I have never done JS testing before, all I did is writting code, run it, if there is bug, figure out, if not, consider it as done.

For small projects, this is ok, cos I can figure out where is wrong quickly, but when I came to a team with medium size project, I realize I should learn how to do JS testing.

So my question is:

[1] Is there a common guideline about the procedures of testing(no need to cover everything, just from experienced engineer daily routine)? Like what to test and how. (some examples with explanation will be appreciated)

[2] I find most posts talking about using Jasmine/Mocha/Grunt/Karma to do test, but without understanding the content and plan, I do not quite understand why should I use them and how. So could anyone give me any example about their usage scene?

BTW, I know this is very newbie question, and probably someone will label this as too broad topic, if so, could you please just talk what you think from any specific point with small example. I will collect all the answers and make summary myself( the most important thing I need to know is what "specific" tests I need to do(Like: a test flow). As for how to do, that is second priority ).

Thanks