Although they can be a bit overwhelming and written in technical jargon, becoming familiar with the Web Accessibility Guidelines (WCAG) is a good starting point for making visualisations more accessible. The guidelines are internationally recognised, adopted and tested. You don’t need to become an expert in WCAG, and you don’t need to know all guidelines by heart to make your visualisations more accessible. But learning about the POUR principles (Perceivable, Operable, Understandable and Robust) and getting familiar with the most important guidelines attached to each of the principles will give you a feel for where a visualisation might fail in terms of accessibility, and how you could improve it.
HTML was developed with accessibility in mind, so using its elements in a semantically correct way is a simple way to guarantee a basic level of accessibility. This applies the context of a visualisation (which should use elements like headers and paragraphs in a correct way, for example), for interactive elements (like links, buttons and inputs) and for the elements in a visualisation itself.
The text and the other elements in a bitmap image (like a JPG or PNG) file are not accessible to assistive technology. Providing a good alternative description can help to overcome this partially, but using the vector graphics native to HTML, SVG and its child elements, can make visualisations a lot more accessible. When used correctly, screen readers can traverse the visualisation itself, and users can navigate between the chart elements and the text it contains.
Providing a table representation of the data contained in a data visualisation, either as a HTML table, or as a downloadable file, improves the accessibility of a visualisation. HTML tables can be traversed by screen readers, and a downloadable file gives users (not only the visually impaired ones) the possibility to explore the data in the way and with the technology that works best for them.