Each email account it set up individually under the Settings >> Mail, Contacts, Calendars. Choose Add Account. There is no need to delete an old account unless you are no longer going to use it.
To switch between accounts in the Mail app tap on the Mailboxes button at the top left (in landscape) or the Mailboxes button in the mail list menu (in portrait). You will see two lists, one for inboxes and one for accounts.
If you choose the All Inboxes (only seen if you have multiple accounts set up), then all incoming mail from all accounts will be displayed. Choose the individual inboxes if you only want to see you new mail in those accounts.
If you choose one of the accounts you'll be able to see all the synced folders for that account; Trash, Sent, Drafts, and other's that you may have created in a computer client or on the web site (which are the only ways you can create them).
There is no need to log in and out of accounts.