Whenever I begin to learn a new language or application, one of the first things I do is to read the entire list of built-in commands and functions. Most languages include common function categories, like string functions, date functions, numeric function (which include aggregation functions), conversion functions, etc. The are variations in syntax, but the basics are usually similar. Just reading the list helps me know where to look when I actually need a particular function.
Then, each environment usually has its own special set of functions that make it unique. In Tableau these are mostly in the area of Table Calculations and Level of Detail (LoD) calculations. These are for the more advanced users, but are extremely valuable.
Which functions you personally use really depends on the types of views and analysis you perform.
I hope that helps.
Bill's approach is solid and I have to agree that it's good to familiarize yourself with the basic built-in functions, and a good document for this is the Online Help doc on the Tableau Knowledgebase: http://onlinehelp.tableau.com/current/pro/online/windows/en-us/help.htm
Beyond that in addition to Table Calculations and LoD Calculations are Bill mentioned, I would also say it's valuable to familiarize yourself with Parameters and Calculations, which can in general be used to alter and customize your data internally, and create an interactive experience by using them as Filters.
Moreso than anything, the important portions of the program are going to be largely based on your needs and goals with the data you're using.