How do I share data/access data between classes that rely on each other?

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C++11

I am teaching myself programming and I am in the middle of making a humongous class. To improve readability and function I want to split some of the functions of this class into smaller classes. I have managed to do this for some tools functions that do not need to be restricted per object and that pass a variable back as needed. However when I am trying to do something a bit more complicated, such as have a class that reads in data and stores it in arrays that my main class can then read from and store what it reads or use what it reads to change a private variable, I am completely stuck.

For example, if I make class Num with public arr1[20] and arr2[20] and two member functions that fill these with 20 numbers, how would I then read a specific cell or read the array with my main class so I can for example take the number of cell 4 and put it into its private variable, or compare arr1[16] < arr1[17] so do this?

Basically, I am having issues with the main class being able to read, copy or compare data from another class.

What I have tried:

I have tried moving various variables and functions in and out of classes, making them scoped to their source while in and out of them... I am just not sure how to make these classes talk to and use each others information, either public or private. Of course I can use set/gets in theory, but I am not sure how to lay those out, or how to lay out the code to allow set/gets to function the way I intend.