Well, that depends on how you doing the redirect from the previous form. How are you posting the search term from the previous form?
It would generally be either a GET or POST method.
To load the textbox you can do this:
txtKeyword.Value = Request.QueryString["txtKeyword"];
txtKeyword.Value = Request.Form["txtKeyword"];
or you could just do the following that will work for both GET and POST params
txtKeyword.Value = Request["txtKeyword"];
And all of these would be put in the pageLoad method.
I hope this helps