Learn Italian: Leggi le istruzioni e dimmi il problema. - Read the instructions and tell me the problem.

It is made from the informal command form of dire (to say/tell), which is di', and the object pronoun mi (to me). When you attach a pronoun to a short, one-syllable command like di', the first consonant of the pronoun doubles. That is why di' + mi becomes dimmi.

Why is it il problema if the word ends in "-a"? Doesn't "-a" usually mean a word is feminine?

Usually, yes! But problema is one of a few special words of Greek origin ending in "-ma" that are actually masculine. Other common examples you might already know are il sistema (the system) and il programma (the program).

Is leggi a command here, or does it just mean "you read"?

It is a command here, but it looks exactly the same as the normal present tense "you read". For verbs ending in "-ere" and "-ire", the informal tu command is identical to the regular present tense form.

What is the singular form of le istruzioni?

The singular is l'istruzione (the instruction). Nouns ending in -zione are almost always feminine, which is why it takes the feminine plural article le here.