How common can this usage be?
Here is the phrase: Trate de prestar atencion durante la leccion... I found other ways to say "pay attention" and the use of the verb prestar was not one of them. Is this really a common way to say "pay attention"?
2 Answers
Yes it is, it is very common if not the most common.
prestar atención = to pay attention
and yes, there's about a million ways to say the same thing, you can use the verbs poner, dar, fijar and probably some others 
I am only a learner, but my first instinct for pay attention would be prestar atención, and I learned other ways after that one, and would vary with them depending on the context, but the first I learned is prestar atención.
This thread has two native speakers from Spain at the end that are worth reading:
http://forum.wordreference.com/showthread.php?t=2828690
TO say some one "pay attention" for example in the classroom is common to say: "Preste (usted) atencion" or " Quiere (usted) prestar atencion" formal use, both are imperative form. Other form would be "(tu)presta atencion" or "(tu)quieres prestar atencion" Or if ypu want to say "obey" is "obedece" or hacer caso, contex classroom.."Haz caso"
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They are not exchangeable. Pay attention= prestar atención; hacer caso de= to do as something/someone says, Pay attention to what you are writing/doing/saying Presta atención a lo que escribas/hagas/digas (subjuntivo)
Pay attention to the time Presta atención a la hora que es
Haz caso a lo que yo te diga=Do as I say Haz caso al profesor=Do as the teacher say and also Pay attention to the teacher (in this case it is interchangeable)
