There are four different way to interact with Master Data Services (MDS) to do things such as create a model, load data into MDS, manage business rules, versioning, etc.

• Master Data Manager Web User Interface (“UI”), also called the Master Data Manager Web Application:  The Master Data Manager web application is used primarily by administrators to perform administrative tasks.  For example, only administrators can create models, business rules, or versions of data.  See Master Data Manager Web Application
• MDS Web Services API (WCF API): The Master Data Services web service contains a complete set of operations that let you write code to control all of the features that Master Data Manager does through its user interface.  See Master Data Services – Working with attributes using WCF API, Getting Started with the Web Services API in SQL Server 2008 R2 Master Data Services
• Stored procedures in the MDS database: There are over 300 stored procedures in the MDS database.  Most of these are executed behind the scenes by the UI or the WCF API.  Only a few are listed in the docs (Staging Stored Procedure, Validation Stored Procedure, Delete a Version).  You can execute the undocumented sp’s if can figure out how they work (and a few 3rd-party products I have seen do just that), but just be aware those sp’s can change in future versions
• MDM tables via T-SQL: If you want to bypass the sp’s and did a little deeper, you can directly access the MDS tables.  Again, it’s risky because the table structures can change in future versions, plus the fact you could make a mess of things if you don’t completed understand how all the tables relate to each other.  See Beginning MDS – Getting at the Data with TSQL (Part 7 of 7), Master Data Services – Find your way through the MDS database schema