Forum; I am a newbie working out a bit of code. I would like to know the best way to use separate .cs files containing other classes and functions. As an example of a basic func
The convention in C# (and many other languages) is one file per class (and usually one class per file). There are certainly exceptions to this rule, but splitting a single class across multiple files should be a rare occurrence, not a standard practice.
You mentioned in a comment that you foresee more "complex operations" than the example you gave. What sort of operations are you envisioning? As long as you're just talking about dealing with form controls, the logic belongs in the .cs file for the form (in this case, MainForm.cs, and not MainForm.designer.cs - as others have said, you shouldn't ever modify the .designer file).
If your form is getting too complicated, then it may make sense to break it up into separate custom controls. This would allow you to keep your source files smaller, but (since each Control maps to a class) you'd be adhering to the one class <-> one file convention.