The top line of notes is the treble clef, and you would use your right hand to play these notes. The bottom line is the bass clef, in which you use your left hand.
Top row = Treble Clef = Right hand
Bottom row = Bass Clef = Left hand
One way as a memorization technique is to see that "treble" and "right" both have R's in them. As for the order of treble vs bass, as to which is the top row, I like to think of the bass being in the basement of a building (ie the bottom floor).
You can think of the treble clef as the main voice of the piece, while the bass clef provides any background notes to give the music more rich depth. In other words, you'll likely hear the treble clef notes more predominantly compared to the background bass clef notes.
Side note: in musical context, "bass" rhymes with "case".