Although I've answered hundreds of questions here in Technology, I'd not ordered anything from Amazon until very recently. It's incredibly simple!
Simply find the first item you want to buy and click 'Add to Basket'. If you want something else, do the same again (and again, and again and . . . if you're buying a lot!). When you've got everything in the basket, click 'Proceed to checkout' and simply follow the instructions.
If you need more detailed instructions, they're here:
http://www.amazon.co.uk/gp/help/customer/display.html?nodeId=502528
but, for me, they make a simple task sound complicated; it isn't!
One word of caution though: DON'T put a tick where it offers free one day delivery with a free trial of 'Amazon Prime'. If you do that you'll be signing up to a service which (after the trial period) costs £49 per year!
Chris