(1) Open a twitter account, obviously. You could even open one just for TriMet alerts and never post to it or lock it down.
(2) Install the Official Twitter app on the iPhone.
(4) Go to the TriMet Profile page in the app (search for @TriMet if you can't find it)
(6) Make sure you are following them, and click on the Cog icon to change the notifications: