The very first thing you need to know is that everything on your page (and for that matter, everything on this site) is organised into MODULES.
In the picture below, the modules on a typical profile page are shown as lightened areas. Each of the modules has a HEADER which shows the name of that module.
(see yellow arrows)
To move them, place your mouse over the module header and you will see arrows appear:
For instance, you may want to have your Latest Activity at the top of your page. So try dragging that module to the top of the center column.
Or, you may wish to display your GIFTS module at the top of your page. So try moving that one.
Whenever you move a module, it will stay in that position and you do not have to SAVE the configuration. It will still be that way when you next come back to your page.