Hello Matthew,
As you mentioned that you're new to ArcGIS Pro and Esri software in general, let me start by saying that the Esri websites contain a comprehensive set of documentation on all our software, APIs and SDKs. Learning a new API or SDK is always challenging, and it's highly recommended that you get to know the actual software application first before you get too deep into trying development with it. This is particularly true for ArcGIS Pro, as the concepts and terminology for Pro are extensive. This said, there are many resources to help you get started. Below are links and suggestions for learning Pro and the Pro SDK.
The ArcGIS Pro SDK Group here on GeoNet will be an important learning resource in its own right, and using the full GeoNet site for information on the the full ArcGIS platform should be helpful. Searching the Pro SDK group for earlier Q&A threads and blog posts are a good way to find resources and answers to your questions.
There is a formal instructor-led training course on the Pro SDK which became available earlier this year:
Extending ArcGIS Pro with Add-Ins -- https://www.esri.com/training/catalog/5875286780ac1ffc066b76e3/extending-arcgis-pro-with-add-ins/
It provides a comprehensive introduction to the Pro SDK.
One of the prerequisites for the Pro SDK course includes having taken the ArcGIS Pro: Essential Workflows course -- https://www.esri.com/training/catalog/5763042e851d31e02a43edcb/arcgis-pro:-essential-workflows/, or having equivalent knowledge. This emphasizes how first understanding Pro, its UI, use and vocabulary are very important for learning Pro SDK add-in design and development.
In preparation for the instructor-led training courses, there are many excellent ArcGIS Pro books and online resources to help get started.
http://pro.arcgis.com/en/pro-app/get-started/get-started.htm
http://pro.arcgis.com/en/pro-app/get-started/pro-quickstart-tutorials.htm
https://pro.arcgis.com/en/pro-app/get-started/overview-of-arcgis-pro.htm
http://www.esri.com/library/brochures/pdfs/arcgis-pro-terminology-guide.pdf
Again, a solid grounding in general ArcGIS Pro concepts, UI and terminology will be important for efficient and successful learning of the Pro SDK.
A couple GeoNet posts from last year that can help you get started with the many Pro / Pro SDK resources:
Getting Started -- https://community.esri.com/groups/arcgis-pro-sdk/blog/2016/06/01/arcgis-pro-sdk-development-series-p...
Learning the Pro SDK -- https://community.esri.com/groups/arcgis-pro-sdk/blog/2016/06/10/arcgis-pro-sdk-development-series-p...
In the Learning the Pro SDK post above, there is a good introductory walk-through of the many online resources, with links to the documentation wiki on GitHub which has ProConcept and ProGuide documents -- these are foundational and key documents for learning with the SDK. You should put the ProConcept Framework document at the top of your reading list, as it provides an intro to working with the Pro Framework, DAML, UI controls, asynchronous programming with the SDK, etc.
Also important will be the ProSnippet pages which provide brief, focused code snippets for tasks, divided by area. The Community Samples are going to be an excellent resource as these are ready to use Visual Studio solutions demonstrating different SDK development areas. All of these resources mentioned are found right from the main Pro SDK landing page at ArcGIS Pro SDK | ArcGIS Desktop.
Finally, technical session videos found on the Esri Videos site should also be helpful: https://community.esri.com/groups/arcgis-pro-sdk/blog/2017/04/04/pro-sdk-videos-from-dev-summit-2017
Here's a Pro SDK resource listing to keep handy: