More a comment than an answer - but I cannot add comments yet: Thanks for your help, the count was the easy part. Just for others that might come here. I hope that it will save you some time.
It took me a while to get the attributes from the rows and to understand how to access them from the data() Object (that the data() is an Array and the Attributes can be read by adding them with a dot and not with brackets:
$('#button').click( function () {
for (var i = 0; i < table.rows('.selected').data().length; i++) {
console.log( table.rows('.selected').data()[i].attributeNameFromYourself);
}
} );
(by the way: I get the data for my table using AJAX and JSON)