ffmpeg - Audio - Add audio to a video file

Adding an audio file to a video is achieved with mapping.

Video files can contain more than just a video and audio stream, they can have multiple audio streams for different language as well as subtitle files.
Mapping for a video stream also contains the different quality and bitrate options.

Example

ffmpeg -i video.mp4 -i audio.mp3 -c copy -map 0:v:0 -map 1:a:0 output.mp4

NOTE: This maps the video to the first video stream of the output (default) and the audio onto the first audio stream in the output file.

This command copies the two files into one without any compressing;
If one file is longer than the other use -shortest which finishes the encoding when the shortest stream ends.