It's done automatically (and there's an option at Checkout to switch between US dollars or the UK currency but I've never used it) with the credit/debit card you've highlighted in your account. Having a calculator handy to get the exact US price isn't mandatory but it helps a little. I've used my US-opened amazon account and US checking account; amazon UK is as simple as the regular amazon, only with lengthier delivery (a week instead of the two days I'm used to) and the need to pay extra attention to the shipping options to make sure you don't accidentally hit a 'Next Day' or uber-expensive delivery option (the default one is usually the better one but there's no set price for shipping; most of the Box Sets I ordered ran me about $5 for the regular week-long shipping). Shoot, when you confirm your purchases in Checkout the price of the item ordered usually drops a few quid/bucks because, since it's an international transaction, the VAT tax on the price of a listed item doesn't apply and comes down (about 8%). Wait 'till something comes up that you want at an obscenely low price, save it to cart and then pounce with a regular amazon account; the rest should be self-explanatory as you go along.
I was as afraid as you when I ordered a rare Melville movie from France (also with my US amazon account but with the language barrier added to the confusion) and look at me know: knee-deep in 'Shogun Assassin' and Mikio Naruse R2 imports but without an import player to watch them.