Generating Authentication Token Using Windows PowerShell script

I am, at best, a novice user when it comes to writing Powershell scripts, so any simplified explanation to this question would be appreciated.
I am accessing one of our vendors API services. In order to access it, I need to generate an authentication token. I have the url to send the request to, and I have the username and password. What I am not sure of, is how to write the script to retrieve the token. Is there a "generic" method to do this?

Again, feel free to break it down to the most basic of terms. I won't be offended. :)

Thank you in advance.