#The professional way
Professionally done, all cameras and audio recorders will have a running (SMPTE) time code, which can be configured in 'free run' mode - meaning the time counter runs regardless whether we record or not (ie, STOP mode).
At the beginning of the shooting day, all recordists (cameras, audio) will sync their clocks. This is done either to SMPTE 01:00:00:00, or to the time of the day.
Then all video clips and audio files (broadcast wave files - BWF, which is just a WAV file with time code imprinted) will be 'timestamped' - the time at which the clip was recorded is part of the file header.
In addition, these recorders allow you to choose the folder and file prefix of the recorded clips. A simple case is when all crew (camera and audio) set this prefix based on the shooting day ('Day01' for example).
Then when the audio and video clips are imported to the video editing software, there's alway an option to 'spot' the clips to their original time code. So this is done automatically.
#The non-professional way
Before the days of digital equipment, the syncing between pictures to audio was done manually with the help of a clapper (clapperboard):
Upon the director's instruction 'Cameras', both the camera men and audio recordists will aim at the clapper; then the clapper is clapped.
Later on, each clip is brought consecutively into the timeline (clips are numbered - there's a way to know which came before the other). The sync is done manually, by finding the video frame at which the clapper jaws are hitting each other; on the waveform display, you can see a transient from the sound the clapper makes. So it's all about moving the audio transient to the clapping frame.
Note that this is done until today, even if all equipment can stamp timecode.