Learn German: Es regnet, also geht man hinein. - It is raining, so one goes inside.

hinein combines hin (away from the speaker) and ein (into). It describes someone moving into a place away from where the speaker currently is (presumably outside in the rain). If the speaker were already inside the dry building watching someone enter, they would use herein (towards the speaker) instead.

Is also a false friend here?

Yes! In German, also means "so" or "therefore," not "also." If you want to say "also" in the sense of "too" or "as well," you would use the German word auch.

Why is the word order also geht man and not also man geht?

In German, the conjugated verb must usually be in the second position of a main clause. Because the adverb also takes up the first position, the verb geht takes the second position, pushing the subject man into the third position.

What exactly does the word man mean in this sentence?

man is an impersonal pronoun meaning "one," "people," or the general "you." It is used to make a general statement about what anyone would naturally do in this situation, rather than talking about a specific person.