In short though you're not going to scroll a grid. You are going to create a grid set to the screen size or smaller. Then put a listbox inside it. You can scroll the listbox easily because that's what it does.
<Grid margin="0,0,0,0" width="480" hieght="800"> <!--These values probably need ajusted-->
<ListBox height="800"> <!--Make sure that it is ENTIRLEY on the screen -->
<TextBlock>Put a ton of text here and see that it scrolls</TextBlock>
<Button>You can put anything in the list boxes</Button>
<TextBox>Even Inputs</TextBox>
</ListBox>
</Grid>
Another viable option that is mentioned below is a scroll viewer which works just as well.