Tableau has a few different products based on functionality, privacy and cost. When you get started with a new program, it is difficult to understand which product is best that fits your needs (and budget!). Here are some specifics about each product that I hope will help you decide which product suits you best.
Tableau Desktop is used to visualize and analyze data, create workbooks, visualizations, dashboards and stories.
Tableau Desktop Professional (but not Desktop Personal) can then publish these to Tableau Server, Tableau Online and Tableau Public.
Tableau Server and Tableau Online allow you to safely distribute the interactive workbooks to the right people. You can edit workbooks, visualizations, dashboards and stories in Server or Online, but you can't produce new ones. The editing options are limited compared to the Desktop.
Server and Online can be used as high-performance data repositories for Desktop users.
Tableau Public is a free tool that is intended for people who want to publish information, accessible to anyone. There are both a Desktop and Online components.
Here is a chart made by John Mathis that I found also very useful:
Download Tableau Desktop
Go to http://www.tableau.com/products/desktop and download a free trial in your computer