There are several ways to add video or audio files to your WordPress posts. If the media is in the supported oEmbed options list (including YouTube, Vimeo, Soundcloud, etc.), your first option is simply to paste the link into your post content. WordPress will automatically embed the media for you.
Another option is, if your WordPress theme includes built-in "Post Options," you can add video or audio as featured media (instead of a featured image). If this option is available in your post, simply paste the media link or upload your own mp3 or video file.