Learn Russian: Если у вас нет оригинала, то мы прочитаем копию. - If you do not have the original, then we will read the copy.

The word нет (meaning "there is no" or "do not have") always requires the following noun to be in the Genitive case. Since оригинал is a masculine noun ending in a consonant, we add -а to make it оригинала.

What is the role of то in this sentence? Can I just leave it out?

то translates to "then" in an "if... then..." sentence structure (Если... то...). While you will sometimes hear Russian speakers drop it in casual conversation, it is very common and structurally ties the two halves of the condition together.

Why use прочитаем instead of будем читать for "we will read"?

прочитаем is the perfective future tense of the verb. We use it here because we are talking about reading the copy completely, achieving a specific result. будем читать is imperfective and would just mean the process of "we will be reading" without focusing on finishing it.

Why does копия change to копию?

копию is the Accusative case of the feminine noun копия. It changes because it is the direct object of the verb прочитаем—it is the thing being read. Feminine nouns ending in -я change to -ю in the Accusative case.