Homography is a projective transformation that displays lines in straight lines, preserves the transverse relation, but does not preserve parallelism or other similarity values (angles, distances, etc.). Homography can be expressed as a homogeneous 3x3 matrix and computed in many (indeed, many) different ways according to your problem.
The most typical is the determination of 4-point correspondences between two planes and the use of direct linear transformation (DLT). There are also many DLT implementations. If you are familiar with OpenCV, you can easily get such a homography matrix using cv::findHomography ( http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html?highlight=findhomography#findhomography ).
In general, I recommend you take a look at the book “Multiple Geometry of Sight” by Hartley and Sisserman, which explain in detail the concepts of homography in the context of computer vision.