To borrow eBooks and audiobooks you need the OverDrive Media Console program or app on your computer or other device, and computer users also need Adobe Digital Editions to view the eBook. Both OverDrive and Adobe Digital Editions are free.  

I joined the City of Edinburgh eBook library to try it out. I went round to the local library and registered and was given a card with a four digit passcode. I logged on to the library eBook web site, downloaded OverDrive to an iPad, and then clicked the 'Get Books' button on the iPad. I browsed through the books available and decided to borrow The Dyslexic Advantage by Fernette and Brock Eide. I typed in my library membership number and the passcode to download it and I've been reading it for a few weeks: lots of interesting and useful insights. It's a big book and I don't have too much time, and when the loan period expires it automatically deletes itself - although you can always go back and extend the loan.

It's a fairly painless process and seems like a good way to access eBooks and audiobooks for free.

A few observations:

• You can't borrow Kindle books (yet - this may happen, but so far Kindle books are only available to US libraries).
• The OverDrive app on the iPad has some features to improve accessibility, although it's quite limited - the maximum font size is not huge (I'd say about 24 point), colour options are only black text on white or sepia, and the font is serifed. However, you can use the iPad built-in white-on-black colour scheme, and have the text read out using VoiceOver. 
• On a Windows PC or Mac, you read the eBook with Adobe Digital Editions (ADE). There are two versions - ADE 1.72 and ADE 1.8 Preview. The latter has accessibility features: on a Windows PC, you can have the book read out with Jaws or NVDA screen reader software, while Mac users can have the text read out using the built-in VoiceOver. You can't read the book with other text-to-speech programs such as WordTalk, Read and Write Gold, ClaroRead etc, and you can't copy or save the text into other programs to have it read out. The font is serifed and you can't change it. You can't change the colours within the program (you can with the computer's own display settings).

See the Books for All Finding Books pages for more on finding books in alternative formats, and particularly the library page for links to library services.