The idea here Michael is to keep everything low voltage and a mains adapter in the house will afford the desired low voltage. A mains adapter can be as simple as what is commonly called a wall wort. The idea is it plugs directly into your house outlet (120 VAC) and typically outputs a low DC voltage like 12 Volts DC. The motion sensor is typically called a PIR sensor or just plain motion-sensor. This is not to say the system must be low voltage DC only to say it's a good idea in the interest of safety. My outside flood lights work off a motion sensor on house mains voltage of 120 VAC.
The problem here is I (or anyone here) could tell you to run out and buy a PIR (Passive Infra Red) motion sensor and start building a circuit. Unfortunately I don't see that going well since you have no experience building electrical/electronic circuits. In the interest of keeping this simple I would suggest a simple motion sensor from any home improvement store such as Lows or Home Depot.
Here is an example from Home Depot. The merit here is it is a packaged turn key solution anyone can install and setup and it is wireless. You will need to run power to your garden area. I suggest using an outdoor approved GFCI (Ground Fault Circuit Interrupt) approved outlet. Following fall harvest the thing can be relocated and used for another application or saved till next season. The idea being keeping things simple and safe.
Ron