Your textbox is a member of the Form1 class, access to it is possible inside the member functions of the Form1 class,
Form1.cs
 namespace WindowsFormsApplication1 { public partial class Form1 : Form { public Form1() { InitializeComponent(); } public void DoSomeStuffWithTextBox() { textBox1.Text = "some text"; } } } 
And on the class object through a point from other classes - is impossible, since the access level of textboxes inserted through the form designer is private
Form1.Designer.cs
 namespace WindowsFormsApplication1 { partial class Form1 { ................................ private System.Windows.Forms.TextBox textBox1; } } 
Although, you can manually change the access level for textBox1 to public in this file;) <crutch />. And, although the file is generated automatically, if you change the form, your editing will be saved (if you do not delete textBox1 from the form, of course).
It is best to make a public method (or property) in the form that returns a reference to textBox1 .
 namespace WindowsFormsApplication1 { public partial class Form1 : Form { ..................... public TextBox getTextBox() { return textBox1; } } }