Learn Russian: Пускай студентка почитает книгу.

Adding по- to the imperfective verb читать (to read) creates the perfective verb почитать. Here, the prefix по- is delimitative, meaning it limits the duration of the action. It changes the meaning to "to read for a little while" or "to read for a bit".

Why is почитает in the future tense if this is a command to do something right now?

In Russian, third-person commands (saying "let him", "let her", or "let them" do something) are built using the particle пускай or пусть followed by a normal conjugated verb. Because почитать is perfective, its conjugated form (почитает) is grammatically future tense. However, paired with пускай, the whole phrase functions as a command for the present or immediate future.

What is the difference between пускай and пусть?

They mean exactly the same thing: "let". Пускай is simply a slightly more colloquial or conversational variant of пусть. You will hear both frequently in spoken Russian, and they are completely interchangeable here.

Why is студентка in the nominative case instead of the accusative?

In English, "the student" is the direct object of the verb "let". But in Russian, пускай is a particle, not an active verb. The core of the sentence is actually студентка почитает книгу (the student will read a book). Since студентка is the subject performing the action of reading, it stays in the nominative case.