When I'm going to do a project how can I know which language (s) to use?
Your browser understands HMTL, CSS and JavaScript, languages like Ruby, PHP, Python, etc., will generate code that browsers understand.
What does one language do that the other does not?
Difficult to compare backend languages, practically all backend languages can do the same thing, the difference is that in some a task can be easier and in others more difficult.
Which language is best for each situation?
If you are going to work with high performance in the backend look for languages like Scala, Java, Erlang. If you are developing projects that you need to develop quickly use PHP, Ruby.
What is the order in which I declare them?
Start with HTML, it will be the structure of your project (imagine a building, first construct the structure, then stylize your HTML with CSS (finishing). Finally create communication with the database through languages such as PHP, Ruby, Python, etc ...
What triggers each one? What does it take for each of them to be initiated? Do they all start together? Do they start apart? Which one starts first? What is the best order to place them? Or does it depend on how you program?
When a user opens a browser and enters a URL, the server receives this information (probably on port 80, http) and initializes the HTTP server (apache, nginx, etc), this server communicates with the application and tries to resolve her returning an answer. There is a life cycle for each request, whether it is complex or not.
How to know when to use each one? (Can you give examples? This is very important to me.)
This is perhaps the hardest question, it depends a lot on the purpose of your project. Start with the basics, and evolve your design accordingly.
I hope I have helped, the questions are very general and difficult to answer.
