Depending on what roles and levels of engagement in the process you are seeking. The absolute basic would be
- understanding of human-computer interaction and user experience,
- designing interfaces keeping those principles in mind
- validating ideas, prototypes with users via one or both of the above and iterating with new data-sets.
There are tons of books and online/offline resources to get started.
With your background in design, you might already be familiar with research, validation, prototyping and user testing etc. In that case, you might be able to focus on how those principles/processes are applied in the context of digital products.
- About Face by Cooper
- Lean UX
- Don‘t make me think
- Apple‘s Human Interface guidelines / Material design guidelines (both are great resources when you start to think about problem solving in visual medium)
- Typography - * The Elements of Typographic Style by Robert Bringhurst
- Save the Pixel
Depending on your familiarity with the subjects, you can add books on Grids, colors etc to the above list.
In the realm of interface design, you can learn about concepts like Responsive Design, Form design, Information and Dashboard design etc.
Will add more resources as I remember.
Product Design would be a broader umbrella term which may or may not involve working a lot with business stakeholders and coming up with features that could lead to growth of the product and business. Often those responsibilities are given to a separate role, that of a Product Manager.