A simple way to do this is to give your textbox a name in the XAML and then access that textbox via the name in the code behind.
<TextBox Name="myTextBox"/>
then in the code behind you can do this
myTextBox.Text = "blah";
A better way is to use binding so that updating the textbox automatically updates the property you are bound to. Have a look at this post textbox binding example
For a rich edit textbox you should be able to do this:
set
myTextBox.Document.SetText(Windows.UI.Text.TextSetOptions.None, "Here is text");
get
string value = string.Empty;
myTextBox.Document.GetText(Windows.UI.Text.TextGetOptions.AdjustCrlf, out value);
See this post for more information