(someone) is amazed at ("how" clause)

Use this phrase to express your surprise and amazement about some quality of a thing:

I was amazed at how easy it was to make.

I'm totally amazed at how you've been able to make connections with so many influential people in just a few months.

In spoken English, you may sometimes hear people leave out the "at":

I'm just amazed how quickly you were able to pick that up.

(something) turned out well

The phrase "it turned out well" means "it was good at the end". You use this phrase to judge a project, an event, or anything that you make. You say "it turned out well" when you think that the end result is good.

Sometimes people use this phrase when a project seemed to be going badly while it was in progress:

I was worried there for a little while, but overall I think it turned out really well.

given the circumstances

You add "given the circumstances" to a sentence when there are problems with something that make it difficult. When you're making a decision about it, you want to consider those problems. So if you're judging how good something was, "given the circumstances" means that you don't want to use a really strict standard for judging it.

For example, if you and your wife are trying to save up money but only one of you works, you can say:

I think we're doing pretty well given the circumstances.

This means that you aren't saving a lot of money, but you are saving a lot for a couple with only one income.

"Given the circumstances" can come at the beginning of a sentence or at the end.