Reading notes
The grand staff
The grand staff is two staves joined by a brace: treble clef on top for the right hand, bass clef below for the left. Middle C sits exactly between them, on a ledger line below the treble staff or above the bass staff: the same key, written two ways.
Read it, then play it
Play the note you see on the staff. The exact key counts: how high the note sits tells you which octave.
One scale across both staves
C major from C3 to C5: it climbs the bass staff, crosses middle C and carries on up the treble staff. Middle C appears on both, once above the bass staff and once below the treble staff.
Which hand reads which staff
The right hand usually plays the treble staff and the left hand the bass staff. It is a habit, not a rule: when a hand crosses into the other's range, its notes can simply move to the staff that reads them best.
Reading both at once
Notes lined up vertically are played together, whichever staff they are on. Read each chord from the bottom up: left hand first, then right hand, the way the sound stacks.
Why two staves, not one
A piano covers more than seven octaves. One staff of five lines would need a forest of ledger lines; two staves a note apart, with middle C between them, keep almost everything readable.