How to get a list of a user's (or channel's) public YouTube videos

The process is quite simple:
  1. Get an API key for the YouTube v3 Data API.
  2. Query the https://www.googleapis.com/youtube/v3/channels?part=contentDetails&forUsername={user_or_channel_name}&key={your_api_key} url and substitute the channel name and api key with the proper values.
  3. Query the https://www.googleapis.com/youtube/v3/playlistItems?part=snippet&playlistId={playlist_id}&maxResults=50&key={your_api_key} url and substitute the playlist ID with the ID of the "uploads" playlist (fetched with the prev. query) and your API key. The result will contain max. 50 videos, but if it's so, there'll be a "nextPageToken" value that you can add to the URL in the "pageToken" parameter and request the next 50 videos, etc.