Basso continuo, sometimes just called "continuo", was played by a keyboard instrument and another bass instrument such as cello, violone (an old form of double bass) or bassoon. The keyboard instrument was normally a harpsichord, or, if it was being played in a church, an organ.
It was not usual to write out all the notes for the keyboard player. The composer normally just wrote the bottom line which would be played by the left hand (usually with a lower 8th doubling) and the other bass instrument. The composer would indicate what the harmony should be (which chords should be played) by writing figures underneath the music.