Finding relationships in datasets and predicting data

I'm a .NET developer trying to learn more about AI/Machine Learning.

I have a dataset with few variables and known results. I'm looking for a language/framework/tool/approach to analyze the data and identify which variable(s) contributed the most towards the results and eventually predict what the result will be given only the variables.

I live in a Microsoft eco-system. Could someone suggest a starting point to research? Does this sound like a common problem?