ChipAHoy, I'm on a Mac, if you can let me know where you're getting stuck I might be able to help out. I basically followed
How To Geek.
Once setup I go to
http://www.amazon.co.uk/mk although yours might be
http://www.amazon.com/my, select the ... next to each book and click DOWNLOAD, it will appear in your DOWNLOADS location in Safari. Then simply drag the file into your Calibre window that's open, it should import the ebook and remove any DRM. I don't use the Kindle app for Mac, I bypass this. Once imported if you have it setup to automatically remove DRM it will remove it. If not you can right click on the ebook in Calibre and select CONVERT BOOKS and CONVERT MANUALLY on each one (or select a bunch and do multiple).
You can then right click on the book again and OPEN CONTAINING FOLDER and it will show you the converted ebooks. I always convert to MOBI and I can then use the Send to Kindle email service to put them back in my cloud or copy them manually to an ereader of my choosing.