How many keys on a piano?

A standard full piano has 88 keys. 52 white or "natural" keys, and 36 black keys, which can be "sharp" or "flat" depending on if the note is high or low. This makes a total of seven full octaves plus a minor third, from A0 to C8

Musically speaking, a sharp is a note that is one half step higher than its natural note. Likewise, a flat is a note that is one half step lower than its natural note.
However, the two terms are also used in general when tuning instruments. If you are sharp you are out of tune on the high side, and if you are flat you are out of tune on the low side.