When you do something amicably, you're doing it politely and nicely. It's best to deal with traffic cops and waiters amicably.
This word for doing things in a pleasant manner is often used in not so amicable situations. Let's say a couple gets divorced — if they parted amicably, then there wasn't a lot of yelling and screaming, and they both agreed to it. You could say two countries that dislike each other had a meeting of their leaders that was conducted amicably: they were polite and said nice things, even though that's not necessarily how they felt.