Learn German: Der Teller und die Tasse sind hier. - The plate and the cup are here.

No, die Tasse is singular here. The article die is used for all plural nouns, but it is also the singular article for feminine nouns. Since Tasse is a feminine noun, it uses die in the singular. If it were plural (the cups), it would be die Tassen.

Why is the verb sind (are) plural if Teller and Tasse are both singular nouns?

Even though der Teller (the plate) and die Tasse (the cup) are singular on their own, the word und (and) joins them together. Just like in English, combining two singular things makes a plural subject (they), so we need the plural verb sind (are) instead of the singular ist (is).

How do I make der Teller plural if I want to say the plates?

For many masculine nouns ending in -er, the plural form is exactly the same as the singular! To say the plates, you just change the article to the plural die, making it die Teller.

Could I say Der Teller ist hier und die Tasse ist hier instead?

Yes, you absolutely could! That means The plate is here and the cup is here. But combining them into one sentence with und and using the plural verb sind is much more natural and saves time.