Previous answer is good, text book, but long way around. (no disrespect :) )
You dont say what Outlook you're upgrading from unfortunatly so I will assume 2010.
File>Info>Acc settings>Acc Settings>Data Files.
Now click the data file(s) AKA PST's one by one , then click Open File Location. Copy these to a new folder / USB. If you want to back them up to a cloud service zip them 1st.
Once that is done, uninstall current Office, reboot, install 2013, let it update, reboot, start email acc setup, I HIGHLY advise using IMAP not POP3, especially if you want to access ALL the mails (IE 1:1 copy if Inbox, Sent Items and customised folders) from multiple devices. In such an instance POP3 will only have a replica of the Inbox.
link for more details - http://www.howtogeek.com/197207/email-basics-pop3-is-outdated-please-switch-to-imap-today/