The precise steps for doing this vary by the desktop software you use but it follows these steps. Note that after August, this does not work for un-official CPCUG.org email accounts.

First, install your selected email software on a desktop or laptop you control, without hooking up any email account until you read through this Answer and determine which of the two approaches below you will use. Thunderbird which is free and works on Windows and Macs is a good choice. Click here for Email Setup Tutorials.

From here there are two approaches, this is the quicker:
Second, hookup any other email account to your desktop email software, perhaps your new email account, following that account providers parameters. For this first approach to work for archiving, that account should use POP3 connections. Once that other hookup is working, add new folders to that account, using your desktop software, one for each folder you plan to archive from our Webmail.

Third, hookup that software to your mailbox at cpcug, using the same procedure but for CPCUG, using the IMAP protocol, not POP3. See also CPCUG Email Server Name.

Fourth, check that you are not logged in via Webmail, and login to your CPCUG.org account using your desktop email software, where you should see all the folders displayed.You can open each folder to see that the contents are as you expect.

Fifth, using the Copy procedure for your desktop email software, copy the contents of each CPCUG.org folder to the corresponding folder for the other email account in this desktop software.  As that other email account uses POP3 (see second step above), those other folders are only on your desktop.

Sixth, some but only some IMAP accounts allow you to load groups of old email to its folders using this Copy procedure in desktop software, assuming the other email account is hooked up using IMAP. For example, you can offload CPCUG.org mail via IMAP but cannot upload it. (The same mailbox should not be accessed both with IMAP and POP3; if you need to alternate protocols change the settings on your desktop email software to be safe.)

The alternative approach is much more time consuming but more general:
Second, hookup desktop software to your mailbox at cpcug, using the POP protocol and not IMAP. (This is the opposite of the second step in the first approach above.)

Third, one of the account setup choices is to "leave messages on the server," or words to that effect. Do not do that; instead leave that checkbox empty. You want the messages moved to your desktop.

Fourth, each time you access your email account with this software, it will automatically download the contents of your Inbox.

Fifth, if you have other folder content online you need to offload, after the Inbox is emptied by the software, logout of your desktop email-software. Then use Webmail to move one other folder's contents to your Inbox then logoff (and see Moving Content in Webmail).. Reconnect using the desktop software, so that content should download to your desktop or laptop. Repeat as needed.

This process cannot offload your webmail address book.