Adding and deleting "data" in Cayenne is done via ObjectContext operations on corresponding "objects". The examples are available in the tutorial here and here and also in the main docs, but here is a quick explanation:
// create new object in memory
Artist a = context.newObject(Artist.class);
// now save it to DB. This will generate INSERT SQL
context.commitChanges();
// delete object in memory
context.deleteObjects(a);
// save this to DB too. This will generate DELETE SQL
context.commitChanges();
And I certainly recommend to go through the tutorial. It shows all the main pieces of Cayenne without giving too many distracting details.