Learning how WolframAlpha works is best understood by understanding how the processing engine behind WolframAlpha works...
The 4 “pieces” of the WolframAlpha Knowledge Engine
1) Data Curation – This is the most unique part about WolframAlpha. WolframAlpha has trillions of pieces of curated data. What this step involves is getting data from a wide variety of sources: free data, licensed data, data from constant feeds, etc… and then taking that data and running it through a partially automated, partially human process so that it is clean, verifiable and computable. A lot of this process can be done mathematically, but at some point you need a human to interact with the data to verify it 100%. In summary, this step has WolframAlpha taking the data and cleaning it up to make it computable and then organizing it logically.
2) Internal Algorithms & Computations – This part of WolframAlpha takes all methods, models, equations from all different kinds of areas of knowledge (like engineering, science, math, etc…) and implements them all inside the Mathematica software that is powering WolframAlpha. The engine does this so that it can do computations about all sorts of things. There are five to six million lines of codes that implement these models and methods in the Mathematica code.
3) Linguistic Understanding & Analysis – This part of the engine is what works to all you to interact with the engine how you naturally think about things – instead of being required to follow some kind of preordained format. This is known as natural language processing, which is mapping the natural language of how we think and speak to the established symbolic representations in #2 above.
4) Automated Presentation – This is the ability to automate the presentation of things. This tells us how to decipher what to actually show people when they type in a query. For instance, we could show thousands of things like multiple graphs, pictures, etc… for a given search, but the trick here is to automatically decide what and how to present the appropriate data. This part of the engine requires a lot of human interaction.