I just received an email saying my Salient theme has an update. I downloaded it, but have been unable to install. Are there any instructions somewhere that I could use to install this update. I have version 8.5.6 installed currently.

I don't think the linked  instructions from http://themenectar.com/docs/salient/updating-salient/#methods  on this page in the Installation section are clear enough: http://envato.github.io/wp-envato-market/ .

So I chose instead the third method you list for updating Salient, but this does not mention what to do if you are using a child theme. I backed up, then followed the method to select a standard wordpress theme in appearance, delete the theme, upload the new Salient 9 theme and activate it. Then I did the same for the child theme. That seems to have worked, but I think you should add the instructions on what to do about child themes to your document http://themenectar.com/docs/salient/updating-salient/#methods and also clarify the installation process for your preferred method of using Envato Market plugin. 

I do realise that it's Envato plugin's documentation that is unclear and not yours, but I presume you can send them feedback as you are promoting their method?

Thanks Imogen