I'm going to split my answer into two parts - design and implementation.
From a design perspective, it's important not to be intimidated by the fact that the users use a computer in a different manner. Treat this like any other project. Observe how they currently use other apps, and ask about the kind of things that they find helpful, or have difficulty with. If they claim nothing is difficult, ask a teacher or assistant, who will be familiar with the kind of things they struggle with.
Once you've started implementation, try an idea and get initial feedback. If you simply ask how they find the prototype, they'll likely say it's ok. Instead, try observing them using it without saying anything or giving guidance. If they get stuck, let them find their own solution to the problem. If appropriate, you could ask the user to speak their thoughts out loud (e.g. "I need to save this form, so I'm scrolling to the bottom, and clicking save").
On the development side, try to use web standards (valid HTML, CSS and Javascript). People often point to the "Web Content Accessibility Guidelines 2.0" (WCAG2) but this is quite turse and hard to understand; there are many more friendly articles on "Web Accessibility".
Someone with a physical disability is likely to use an alternate input device, such as a "Switch", onscreen keyboard, head-tracking device, a device for pushing keys on the keyboard, or speech recognition. Many of these methods involve simulating the keyboard, so by far the most important thing is to consider the accessibility of your site without using a mouse. For example, try tabbing through the page to see if you can access all elements in a reasonable amount of time. Consider using the acesskey attribute to provide an easy way to jump to different parts of the page (using 0 through 9 is often recommended so you don't interfere with browser shortcuts).
Also make sure that no part of your site is time-dependant, as different users may take different amounts of time to perform a task. For example, don't use the onchange Javascript event to update a page based on a listbox selection. Ensure you have alt text for images, so it's accessible for speech recognition. make the pages short enough so that excessive scrolling isn't required, but not so short as to require following lots of links.
Those are just some ideas to get your mind going in the right direction - but there are many accessibility resources on the internet - steal freely, and don't reinvent the wheel.
I realise I haven't addressed your question about Javascript - that's because I think it's probably one of the less important considerations. If possible, use Progressive Enhancement techniques to make the site work with and without Javascript. You might also look into the WAI-Aria standard for giving semantics to your Javascript.
And finally, to reiterate my initial point - make something simple, show it to the users, tweek, and show again.