Looking at the piano you'll notice that it's made up of a repeating unit: the black keys seem to repeat, with a group of 2 "black notes" followed by a group of 3 "black notes", followed by another group of 2, another group of three, et cetera.
Pick any of the "2 black note" groups. The white key to its immediate left is called C. Then, counting up the white notes, the successive keys are: C, D, E, F, G, A, B, and then C again.
In some European countries, the notes are named instead: do, re, mi, fa, so, la, si, and then do again. Also, often when singing out notes the do re me convention is adopted. Instead of singing out, say, C F G, you'd sing out do fa so.
The black key to the immediate right of a white key is given the white key's name with a "sharp" suffix, marked with a "#". Similarly, a black key to the immediate left of a white key is given the white key's name with a "flat" suffix, marked with a "b".
The note names on the piano are then, starting from C and advancing to the "right" (including black notes): C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C This is entirely equivalent to: C, Db, D, Eb, E, F, Gb, G, Ab, A, Bb, B, C So some notes are interchangeable: C# = Db D# = Eb F# = Gb G# = Ab A# = Bb
Source Mangold Project