How to determine what type of monitor I have?

To determine what type of monitor or display you are using generally requires that you physically look at the front and/or back of the monitor. Many times the manufacturer of the monitor will be listed on the front of the monitor. Additional information and monitor and specifications for computer monitors are commonly found on the back of the monitor.
If you are unable to locate the size of the monitor, this information can be obtained by measuring from the bottom left of the monitor screen to the top right of the monitor screen. 

Reasoning:

Product listing or specifications

If you are trying to list all the specific information about your computer, specifying the manufacturer and size of the monitor is sufficient. For example:

19" Optiquest monitor

Replacement or repair

If you are trying to determine the type of monitor because it needs replaced or repaired, it is recommended that you determine the cost of having the monitor repaired by contacting a local monitor / TV repair shop. If the cost seems excessive for the type of monitor, it is recommended that you simply purchase a new monitor.