How to access form methods and controls from a class in C#?

You are trying to access the class as opposed to the object. That statement can be confusing to beginners, but you are effectively trying to open your house door by picking up the door on your house plans.

If you actually wanted to access the form components directly from a class (which you don't) you would use the variable that instantiates your form.

Depending on which way you want to go you'd be better of either sending the text of a control or whatever to a method in your classes eg

public void DoSomethingWithText(string formText)
{
   // do something text in here
}

or exposing properties on your form class and setting the form text in there - eg

string SomeProperty
{
   get 
   {
      return textBox1.Text;
   }
   set
   {
      textBox1.Text = value;
   }
}

Another solution would be to pass the textbox (or control you want to modify) into the method that will manipulate it as a parameter.

public partial class Form1 : Form
{
    public Form1()
    {
        InitializeComponent();
    }

    private void button1_Click(object sender, EventArgs e)
    {
        TestClass test = new TestClass();
        test.ModifyText(textBox1);
    }
}

public class TestClass
{
    public void ModifyText(TextBox textBox)
    {
        textBox.Text = "New text";
    }
}

1. you have to have a reference to the form object in order to access its elements
2. the elements have to be declared public in order for another class to access them
3. don't do this - your class has to know too much about how your form is implemented; do not expose form controls outside of the form class
4. instead, make public properties on your form to get/set the values you are interested in
5. post more details of what you want and why, it sounds like you may be heading off in a direction that is not consistent with good encapsulation practices