One way to do this is to make the TextBox either a public property or a public field. Then you will be able to access it through the instance of its parent form. So, if TextBox1 is a public member of FormA and myFormA is an instance of FormA, then you can use code such as
[VB.NET] Dim strValue as String = myFormA.TextBox1.Text [C#] string strValue = myFormA.TextBox1.Text;
anywhere myFormA is known. Here is a VB project illustrating this technique.