How do I change my SharePoint site homepage's layout?
Click on Page at the top left of the screen and select 'Edit Page'.
The page editing screen will appear:
Move Web Parts
Click and hold, then drag the web part until the little blue marker is in your chosen location (you may need to do this in two parts, scrolling up in between, if your page is long).
Remove Web Parts
Place your mouse to the right of the heading of the item you want to remove.
You should now see a check box and a down arrow indicating a drop-down menu (in the top right corner):
Click on the drop-down menu and choose Delete.
Click OK to confirm on the message that appears.
Repeat the process to remove any other items you do not need.
Check how the page looks
Click on the red Stop Editing button on the top left:
Click 'Browse' at the top left of the page.
View your page as users will see it to make sure it is laid out as you wished.