It depends on your operating system.
Basically make a copy of your entire EQ install by copying the directory. Rename it EverquestB or something so you can tell which is which.
Put a new shortcut to Everquest.exe in the new directory and once one "box" has loaded start the other. Don't try loading both at once as even once the patcher is finished it slows you down enormously.
If you prefer use EQWindows which has better control over 2 windows. Download the program from
here.
You will not be able to run side-by-side and will need to disable sound in one of the directories (use Options when starting to do this).
If you are running XP then you need to download the Microsoft Application Compatibility Toolkit and disable the entry for EQ as it prevents using Alt-tab to change windows.
You may need to reduce options to lower the resource requirement. You will need a minimum of 512Mb RAM and 1Gb would be better. You may get it to run with less by using old models and low resolution and details but what's the point then.
EQWindows seems to give smoother switching. Before I started using it I could be running fine and suddenly a box-switch would take 2 or 3 minutes with disk thrashing while windows confused itself. If you are tasking for a quick heal this can be a bit annoying.
You will get lag between boxes if you try and do things like autofollow. You can overcome this by switching to the follower's view and back or possibly by adjusting the foreground ssettings for XP/EQ (not something I feel competent to do).
Hope this helps