Using internal tables is no different in ABAP Objects to procedural ABAP coding. You cannot use old internal table style with header lines. Use work areas instead of header lines.
CLASS a_class DEFINITION.
PUBLIC SECTION.
TYPES: a_type TYPE STANDARD TABLE OF atable. "From ABAP Dictionary Table
DATA: a_tab TYPE a_type.
METHODS constructor.
ENDCLASS.
CLASS a_class IMPLEMENTATION.
METHOD constructor.
SELECT * FROM atable INTO TABLE a_tab.
...
ENDMETHOD. "constructor
ENDCLASS.
START-OF-SELECTION.
DATA my_class TYPE REF TO a_class.
CREATE OBJECT my_class.