How do I use the Neural Machine Translation (NMT) capabilities in Trados Studio 2015 or Trados Studio 2017? 

You need to have a valid Language Cloud Machine Translation subscription. Either the Free one, or a legacy package that was migrated to NMT. 
Then you need to install to Language Weaver Cloud plugin that allows connection to the NMT models from within Trados Studio 2015 or Trados Studio 2017.

The UI option SDL Language Cloud no longer works within Trados Studio 2017 and 2015, you have to install the Language Weaver Cloud plugin which will then give you the UI option SDL Machine Translation Cloud Provider.

You can download the needed installers from the attached archives to this article.
Please note that these versions of Trados Studio and their corresponding Language Weaver plugins are end-of-life and are no longer supported. 

Installers are also available here: 
https://community.rws.com/product-groups/trados-portfolio/rws-appstore/w/wiki/6453/archived-versions-language-weaver

Installation for Trados Studio 2017 SR1 CU17 or higher

1. Download and save on your computer the installer
2. Close all RWS programs, and install the plugin by double-clicking on it
3. Open Trados Studio and go to Project Settings > Language Pairs > [...] >Translation Memory and Automated Translation and remove RWS Language Cloud as MT provider (if present)
4. Go to Use... and choose SDL Machine Translation Cloud provider from the list
5. Login using your credentials

Installation for Trados Studio 2015 SR3

1. Download and save on your computer the installer
2. Close all RWS programs, and install the plugin by double-clicking on it
3. Open Trados Studio and go to Project Settings > Language Pairs > [...] > Translation Memory and Automated Translation and remove SDL Language Cloud as MT provider (if present)
4. Go to Add and choose SDL Machine Translation Cloud provider from the list
5. Login using your credentials