Most faculty and some grad students currently have two email mailboxes: A <username>@oregonstate.edu and a <FirstName>.<LastName>@oregonstate.edu
The First.firstname.lastname@example.org is a Microsoft Exchange email account. It can be accessed by going to exmail.oregonstate.edu and can be added to most email clients.
The email@example.com is either an imap account or a Google account. Google accounts mailboxes can be accessed by going to mail.google.com and logging in using firstname.lastname@example.org. This should redirect you to the normal OSU sign-in page. If you get a message saying that this service is not enabled for your account then you likely have an imap mailbox instead.
IMAP mailboxes can be accessed by going to webmail.cosine.oregonstate.edu.
In addition to those two mailboxes, you may also have aliases to those mailboxes. This usually looks something like: <username>@math.oregonstate.edu or <username>@geo.oregonstate.edu These aren't sepperate mailboxes, rather any mail sent to them is automatically forwarded on to your <username>@oregonstate.edu.