Using microphones and computers, we can layer sounds on top of each other, even if they were recorded at different times. All of the instruments in this video were played by one person, and all of the voice parts were sung by one person. These two people didn't write this song, but since they liked it so much they decided to record their own version.
Here are some recordings of me playing a whole bunch of instruments at once. Most of them are just regular classroom instruments. (Mrs. Peters did the singing.)