Like is generally used to compare nouns.

Lisa is like a bird, constantly soaring to new heights.

That explanation is not complete, however, as there is an exception.

The following works.

Jim thinks like Einstein.

We have noun verb compared with a noun.

In this case, like Einstein means in the manner of Einstein.

Here is something that you can count on though.

As is always used when you have noun verb noun verb.

Bob runs as John does.

Noun: Bob Verb: runs AS Noun: John Verb: does

The people of the United States still play as they have for ages.

Noun: people Verb: play AS Noun: (pronoun) they Verb: have

From the question:

In Turkey, coffee is traditionally drunk very strong, much as it is in France.

Noun: coffee Verb: is drunk AS Noun: (pronoun) it Verb: is

Works like a charm!