I assume your button is out side the grid view and only one check box can check in the grid view at once.
if so inside the button click event. you need to loop the grid view for find the checked item.
foreach (DataRow dr in DetailsView1.Rows)
{
}
then there is 2 ways to display in other page.
1) take all row data in to current session and the on the next page show those data.(ex: to string[] and then put in to the session)
2) take only id of checked item and put in to the query string or session and then retrieve on next page. using that id you can retrieve data belongs to particular id and display where ever you want.
hope this will help...
if you need more code level help please noted...