Day after day, the dog sat in front of the station waiting for its master.

Literal

Come day [also-も] come day [also-も], that dog [topic-は] station [possessive-の] front [at-で] master [object-を] wait-[while-て] was-sitting.

A second Hachiko-referencing sentence. 待って座っていた is a te-form + ongoing form: 'was sitting while waiting.' Note the structure: 座る ('to sit') as the main verb holding the ~ている aspect, 待つ as a subordinate te-form action.