Learn English – How to use “have been” and be-verbs — what’s the difference between them

More idioms.

"I have been to somewhere" means that I have gone there and come back. But you can only use this in the perfect (present, past or even future): it isn't available in any other tense:

By the time I was twenty I had been to China.
By next autumn I will have been to China.

but not:

*I am to China.
*I will be to China.
*I am being to China.

The special meaning relates to the word 'been', not any other parts of 'to be'.

In most uses, "go" is unspecific about whether or not there is a return journey:

He's going to China next month.

is probably a trip, but could be emigration.

The case of "gone" brings in the special properties of the perfect. "He has gone" is talking about a state of affairs that includes, or relates to, the present. The most obvious interpretation of

He's gone to China.

is that he is still going, or still there. But as Robusto says the present-relevance could have a different interpretation, so

He's gone to China several times.

necessarily means that he must have returned (or gone somewhere else), so the present relevance is that the sequence of trips is seen as continuing. Contrast

He went to China several times.

which implies that the series of trips is over, and he is not going again.

(These are implications, and may be overridden by other words or by context; but in the absence of anything to the contrary, the sentences will have the meanings I am suggesting.)

In can be used instead of for only in the second example. The other sentences can have only for to be correct.

Edit upon comment: In can be used to show the same thing after first, last, etc as in:

It's the first email I've had in ten days.

And as it's been pointed out, when the sentence is negative, in and for are interchangeable.