This is a huge topic, with answers from 3 lines of code to entire research magazines.
I will outline the most common such techniques and their results.
Comparing histograms
One of the simplest & fastest methods. Proposed decades ago as a means to find picture simmilarities. The idea is that a forest will have a lot of green, and a human face a lot of pink, or whatever. So, if you compare two pictures with forests, you’ll get some simmilarity between histograms, because you have a lot of green in both.
Downside: it is too simplistic. A banana and a beach will look the same, as both are yellow.
OpenCV method: compareHist()
Template matching
A good example here matchTemplate finding good match. It convolves the search image with the one being search into. It is usually used to find smaller image parts in a bigger one.
Downsides: It only returns good results with identical images, same size & orientation.
OpenCV method: matchTemplate()
Feature matching
Considered one of the most efficient ways to do image search. A number of features are extracted from an image, in a way that guarantees the same features will be recognized again even when rotated, scaled or skewed. The features extracted this way can be matched against other image feature sets. Another image that has a high proportion of the features matching the first one is considered to be depicting the same scene.
Finding the homography between the two sets of points will allow you to also find the relative difference in shooting angle between the original pictures or the amount of overlapping.
There are a number of OpenCV tutorials/samples on this, and a nice video here. A whole OpenCV module (features2d) is dedicated to it.
Downsides: It may be slow. It is not perfect.
Over on the OpenCV Q&A site I am talking about the difference between feature descriptors, which are great when comparing whole images and texture descriptors, which are used to identify objects like human faces or cars in an image.