Learn Italian: Scrivo una parola sul foglio. - I write a word on the sheet of paper.

In Italian, when the preposition su (on) is followed by the definite article il (the), they combine into a single word. Su + il always becomes sul. You will almost never see them written as two separate words.

How would this change if I were writing on multiple sheets of paper?

You would change the noun to the plural fogli, and update the combined preposition to match. The plural word for "the" here is i. When you combine su + i, you get sui, so the phrase becomes sui fogli.

The translation says "sheet of paper". Can I use the word carta instead?

Carta refers to paper as a general material (like saying "it is made of paper"). When you are talking about a specific, countable piece or "sheet" of paper, you must use the word foglio.

Why isn't the word io (I) at the beginning of the sentence?

In Italian, you usually drop the subject pronoun because the verb ending already tells you who is doing the action. The -o ending on scrivo means it can only mean "I write". Adding io is unnecessary unless you really want to add special emphasis.