The -고 clause supplies the vehicle or the step before: 저 이제 기차 타고 내려갑니다 "I'm taking the train down now", 엘리베이터 타고 내려가면 "if you take the lift down". In Korea 내려가다 also means leaving Seoul for the provinces, which is what the train and car lines here mean — the mirror image of 올라가다. It works for drink as well: 목을 타고 내려가는 맛, the taste as it goes down your throat.