I'm taking further intro java classes at the moment and this is how the class briefly defined this:
Cohesion: Aim for high cohesion, in this case cohesion meaning that a single module is tightly focused on its task.
Coupling: Aim for low coupling, in this case coupling meaning the level of extent in how intertwined two or more modules are.
How does one determine the level of cohesiveness as well as coupling?
For instance, some of my methods call other methods that are in the same class. This means that the method that calls other methods are dependent on the other methods in order for the "calling" method to finish its code block. Does this mean that I have low cohesion and high coupling on the methods of the same class? Or do these concepts refer more to different classes and different packages?
There are metrics for cohesion / coupling; see https://softwareengineering.stackexchange.com/questions/151004/are-there-metrics-for-cohesion-and-coupling.
So the way to "determine" the level of cohesion / coupling is to implement a tool that measures the respective metrics. (Or find an existing tool that does this. For example, Sonar.)
I assume you mean ... how do you decide when you will call values of the respective metrics "unacceptable" in your codebase.
Basically, that is up to you to decide. I would do it by looking at examples where the tool is reporting a "bad" value, and decide how bad I thought it really was. Alternatively, stick with the default thresholds in the tool that you are using.