i) Put the search criteria if short into query string or else add them to session variable.
ii) Now redirect to the particular page i.e. search.aspx here.
Ex :-
Response.Redirect("~/SearchResult.aspx?name=smruti");
iii) Now on load of the search page get the search criteria values from query string or the session variable and do the search operation to populate the grid in the same page with the search results.
Ex :-
protected void Page_Load(object sender, EventArgs e)
{
string name = string.Empty;
if(Request.QueryString["name"] != null)
{
name = Request.QueryString["name"].ToString();
}
}
Hope his will be of help.