this is not a problem, just logical & business, for search button can be done like below:
Response.Redirect("your_search_page.aspx?ID=" + txtSearch.Text);
so in "your_search_page.aspx", you can write a Page_Load event like:
string query = "select * from Products where ProductID = '" + Request.QueryString["ID"] + "'";
notes: i don't recommend you create an query by concat strings, the better way is use query string with parameter or store producer