Well I have installed cameras before, They do make cameras for that very thing. Here is another way to actually catch the person in hand also
Take a motion light.. The kind people have outside and when it detects motion a light will come on.. Well take the light out of the socket, Replace the light with a socket adapter that you can plug an extention cord into. Then take the extention cord and run it into the house, Hook it to a radio. When someone is in the yard a light wont come on but a radio in the house will come on letting someone know they have visitors in the back yard.
Now back to Cameras. The type of camera you need for this is not going to be cheap for a couple reasons, 1. most outside cameras are pretty high priced 2. Just the lighting will be another factor towards price.
If you do put a camera up, If the cameras not really an infrared camera to see into the dark may pick something up but only like a shadow if that..
But the cheapest affective way is to put a motion setup out there and when somone is in the yard will alert someone in the house and whoever is prowling around in the yard will be more apt to getting cought..