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SIFT consists of two stages- 1) key points detection (2) generation of descriptors . To detect the key points, the input image is convolved with Gaussians, SIFT then looks for local maximums. To generate the descriptors, SIFT calculates a histogram of oriented ingredients around each key point.

http://www.scholarpedia.org/article/Scale_Invariant_Feature_Transform ,http://correll.cs.colorado.edu/?p=2048 gives some brief and informative content about SIFT.

SIFT is quite an involved algorithm.To help you out I have split the algorithm into multiple parts. Here’s what exactly happens in SIFT: Constructing a scale space – This is the initial preparation. You create internal representations of the original image to ensure scale invariance. This is done by generating a “scale space”. LoG Approximation – The Laplacian of Gaussian is great for finding interesting points in an image. Finding keypoints – With the super fast approximation, we now try to find key points. Get rid of bad key points – Edges and low contrast regions are bad keypoints. Eliminating these makes the algorithm efficient and robust. Assigning an orientation to the keypoints – An orientation is calculated for each key point. Any further calculations are done relative to this orientation. This effectively cancels out the effect of orientation, making it rotation invariant. Generate SIFT features – Finally, with scale and rotation invariance in place, one more representation is generated.