First: Have a read about the responsibilities of Model View and Controller. There's a reasonable explanation with an example at this site: http://tomdalling.com/blog/software-design/model-view-controller-explained/
With regard to the Model and your ORM - the ORM would probably exist within the Model. So you should be asking your Model to create a new object (which may represent a single table or a series of related tables - your Model should understand these relationships). You can then pass data to your Model and your Model should then store the data into the appropriate columns in the appropriate tables. A simple example, imagine creating an object called 'Family' where you might specify 2 parent names, a variable number of children names and then tell the Model to save this. The Model may take this 'Family' object and create a single Family table record and 5 Person table records, flagging some as parents and others as children.
Second: The 'Storage Methods' referred to are (in my opinion) referring to the database you use. For example I know that Propel supports MySQL, PostgreSql, MSQL, Oracle, and others. My switch the configuration to a different database Propel will automatically start talking the appropriate language for the new database.