Learn Arabic (Modern Standard): ما هذه؟ هذه ورقة صغيرة.

هذه is the feminine form of 'this'. We use it here because the noun it refers to, ورقة (paper), is feminine. You can usually spot a feminine word by the taa marbuta (ة) at the end.

How do we know to use ما for 'what' instead of ماذا?

In Arabic, ما is used to mean 'what' when you are asking about nouns or using a sentence without a verb, like 'What is this?' (ما هذه؟). You use ماذا when asking 'what' alongside an action word (a verb).

Why does the adjective صغيرة (small) also end in the letter taa marbuta (ة)?

In Arabic, adjectives come after the noun they describe and must match its gender. Since ورقة is feminine, the adjective must also be made feminine by adding a taa marbuta to the end, making it صغيرة.

I don't see words for 'is' or 'a'. How does the second sentence translate to 'This is a small paper'?

Arabic does not use a word for 'is' in simple present tense sentences, and there is no Arabic equivalent for the indefinite articles 'a' or 'an'. Therefore, simply placing هذه (this) right before ورقة صغيرة (small paper) naturally forms the complete sentence 'This is a small paper'.