The following is a quick guide to get this working on various Linux distros. As a side note, if you have Chrome installed alongside Vivaldi, Netflix should also work after making these changes. Alternatively, use my latest-widevine.sh to fetch and extract Chrome's copy of Widevine, so that it can be used by Vivaldi.
If you don't have working Flash video and need that in addition, please refer to these instructions.
Note: This guide is primarily aimed at users of Vivaldi stable releases. If it does not solve your issues, read this in addition.