You look tired, so you should go to bed early.

Literal

Tired-looking [because-から], early bed [into-に] attached [better-方がいいよ].

疲れているようだから uses ~ようだ ('seems like') with ~から ('because') to link the observation to the advice. 床につく means 'to go to bed' — literally 'to attach to the floor/bed.'