To monitor a location over a continuous basis you can use a fixed camera that transmits to a single monitor. This is the same type of Closed Circuit TV (or CCTV) system used by security operations worldwide.
Digital technology has vastly improved the versatility of this method, as digital images can be taken at a much higher resolution, and the footage is easier to study and store.
You can get a quality video surveillance camera for $50-$120 that includes audio as well, with color image and night vision at the higher end of the scale. Installation is a straightforward process.
If the unit will be exposed to the elements, make sure you are purchasing a system that is weatherproof.
Double that price and you’ll find a remote controlled camera that can swivel 360 degrees and see in the dark. If you are after a cheap and easy security device, you may even want to consider a dummy video camera, which uses motion detection to pan an area (and flash a green LED light) in order to appear as if it is actively recording. You can find one for under $30.