In Order to connect dual monitors to a desktop computer, you have broadly two options depending on what do you want do with dual monitors.
In case you want only to duplicate display of your main monitor to another monitor, you would need an extra monitor, connecting cables with appropriate port and a video splitter. The Video splitter is an external hardware device which can be used to duplicate your computer’s output to dual or multiple monitors. The data cable connections from computer to monitor will be so that a data cable will connect your computer to video splitter and all monitors will be connected to the Video Splitter.
You can also visualize it as one to many connections. In order to look for a video splitter, you can even use the word Display Switch, although display switches can be real complex and costly as well, however a simple one to many video splitter should be really cheap and readily available.
In case you would like to control dual monitors by extending your desktop area to the other monitor, move window to second monitor and even duplicate output of your computer to both monitors, you would need a dual monitor graphics card, required monitors and associated cables. You can browse to the post named as Hardware for Dual Monitor Computer to know more about this option of connecting dual monitors to a desktop computer.
You can even have a look at the Dual Monitor Software to know what options you can have to control and manage dual monitors. Once you have got 2 Monitors connected to a Desktop computer, the one with Start Menu would be referred to as Primary Monitor and the other one would can be referred to as Secondary or Second Monitor.