The process is nice and easy once you learn your way around the system preferences. Go to the Apple Menu and select System Preferences. Then displays. It will auto detect the two monitors. You can drag the monitors around to have one on the left and the other on the right, switch around, mirror, set the second monitor as a TV or projector, etc. Play with it. You can not hurt the monitor by experimenting with settings. If you choose a setting that is out of range for the monitor, the system preference will reset to the old setting.
As for a cheap second monitor, CRTs are being given away. Recyclers will refurbish a used LCD monitor with new capacitors and charge $50 - $75.
PS This page shows the options for video. A DVI adapter is included, a VGA adapter is sold separately. So, a free CRT monitor and an adapter sold separately might add up to a refurbished LCD.
Basically you get dual monitors using the mini's Hdmi port and the thunderbolt/mini display port. You buy/use the appropriate adapters for your monitor. Bear in mind that the max resolution is different on the two ports -- see the specs:
Which Eizo monitor do you have? With some of the monitors, particularly the wide gamut monitors you get more colors with displayport as opposed to DVI. In those situations I would get a displayport cable and hook the Eizo up to the mini's thunderbolt/displayport port, that's what I do with my Eizo. Check the specs of your Eizo.