Hope it may satisfies your need.
Hiren's Answer is also an beautiful one.
For Assumption:
In Form1 Declare
public static string TextboxText;
If i Click on Button1 of Form1
i am going to Capture Textbox1.Text in TextboxText
ie
TextboxText= Textbox1.Text;
When i open Form2
Just assign TextboxText to Textbox2 in Form2
ie
Textbox2.Text=Form1.TextboxText;