The fact that you even ask that question is scary.
1) Do you understand what a network is?
2) What OS is your PC running?
3) What OS is the PC you are attempting to access running?
4) Is this "someone else's computer" a mail server or a users personal
PC that had previously download mail that you now want to access?
5) If this is a mail server, what protocol are they employing?
6) Are any firewalls in place?
7) I am assuming that you are using some version of MS Outlook. Is the
"someone else's computer" using the same MUA?
Do you only want to have a quick look at any newly received emails or do you
want to use Outlook for an extended period of time on that computer as well?
Assuming the first, it would be better to use the web interface provided by
your ISP or your company to access your mailbox.
If the second, then you'll have to configure Outlook on that machine as well
by using the mail settings needed for your account. If this is a POP3
account, make sure you set it to leave a copy on the server. For more
details see; http://www.msoutlook.info/question/160