First off, you can call the application "Mail." By default, "us" OS X users know that when Mail has a capital "M," that means the application Mail (or the Mail folder, which I will describe below), as supposed to generic mail. So no need to go ".app" on us.
Second, by "old account" and "new account," I'm not sure if you're talking about OS X accounts, or mail accounts. I'm going with OS X accounts, because you mentioned the keyword "user" when you said "new user."
So, given that you have a new account set up in OS X, your saved messages are located in: [old user account]/Library/Mail/
i.e. inside Library is a folder named Mail. Drag that Mail folder right into your new user account under [current user account]/Library/. Mail (the application) should import all the messages from within the Mail folder upon relaunching the application. So given that you are logged into your current user account, once you've done the drag - one step - launch Mail and you should have all those messages show up in Mail.
Note: Inside that Mail folder are configurations, settings, and your messages for each account you set up in Mail.