How do I actually design for accessibility?

You already care, which is the part most people skip. What you are missing is not heart but method, and method can be learned quickly. Accessibility is not a mysterious specialty. It is a handful of concrete habits applied over and over. Start with the ones that cover the most ground. Enough color contrast to read easily. Text that scales without breaking. Everything reachable by keyboard, not just a mouse. Labels on your buttons and images so a screen reader can speak them. Most real barriers come from missing these few things. Pick one screen you have already made and check it against just those four. Fix what fails. Doing it once on something real will teach you more than any checklist you read in the abstract.