As part of the SQL Server 2012 release Microsoft has released sessions on the Microsoft Virtual Academy one of the is sessions is 7 Module session on Breakthrough Insights using Microsoft SQL Server 2012 – Analysis
One of the session there is one I did together with my colleague Howie Dickerman called: Enriching your BI Semantic Models with Data Analysis Expressions. This will give you a basic understanding of DAX and will go through the new features of DAX for SQL Server 2012.
Enjoy !