Numbered Notation (also called Jianpu, 简谱) writes each melody note as a number from 1 to 7 instead of a note on a staff. The number shows the note's position in the song's scale -- not its exact pitch -- so the same tune looks identical no matter what key it's sung in.
Within one octave, the numbers 1 2 3 4 5 6 7 correspond to the familiar do re mi fa sol la ti. A dot above a number raises it an octave higher; a dot below lowers it an octave lower -- no dot means the middle, as-written octave.
A plain number lasts one beat. A dash (-) right after a number holds that same note for one more beat. A line underneath a number shortens it instead -- one line is half a beat, two lines a quarter of a beat. A 0 is a rest: silence for one beat.
The label at the top of the sheet, like "1=C" or "1=Ab", shows which pitch scale degree 1 ("do") is tuned to. A song in a minor key is labeled "6=X" instead -- scale degree 6 ("la") is the true tonic. Chord names printed above the notes (like "C" or "G7") always use their familiar letter names, never numbers.
For example, under a "1=C" heading, the numbers 1 2 3 4 5 6 7 sound as C D E F G A B. Under a "1=G" heading, those very same numbers sound as G A B C D E F# instead -- same shape, different key.