To start with the xrandr usage, simply enter xrandr (or xrandr -q) to see all available outputs and their current status.
Displayed are the different connectors (i.e. VGA-0, DVI-0, S-Video, LVDS) along with the automatically detected resolutions using the EDID information obtained from the display. The asterisk denotes the current resolution. Other bits of information are also displayed for connected displays. In the above example you can see the display was running via DVI at 1280 x 1024 with a refresh rate of 60Hz. For basic information regarding xrandr see man xrandr or xrandr --help.
When connecting a new display device to the graphics card with X already running, in many cases it's as easy as just entering: xrandr --auto. The auto command will attempt to enable all attached outputs. Connected displays are then treated as one large virtual screen. If there is an output you are looking to disable, such as the monitor connected to DVI-0, the syntax is: xrandr --output DVI-0 --off. If the display order does not align with your monitor configuration, you can change it in the using the --left-of or --right-of syntax: xrandr --output VGA --auto --right-of LVDS.
If xrandr defaults to an undesired resolution, it can be dynamically changed by entering xrandr --output DVI-0 --mode 0 for the first mode listed when running xrandr or xrandr -q. Alternatively, the desired resolution can instead be entered as the argument for mode. The refresh rate can be changed using the --rate argument.