Learn Turkish: Bu ağaçlar büyük, şu kuşlar küçük. - These trees are big, those birds are small.

This is because of 2-way vowel harmony. The plural suffix is either -lar or -ler. To choose, you look at the last vowel of the word. Ağaç has the vowel 'a', and kuş has the vowel 'u'. Because 'a' and 'u' are both back vowels, they take the -lar suffix.

Since the translation says 'these trees', shouldn't the Turkish use the plural word bunlar?

No, in Turkish, when you use a pointing word like bu (this) or şu (that) right before a noun to describe it, the pointing word must stay singular. You only make the noun itself plural. So, bu ağaçlar translates perfectly to 'these trees'.

Why is there no word for 'are' in this sentence?

In simple Turkish sentences, the verb 'to be' (am/is/are) is often completely invisible for the third person (he/she/it/they). You just put the subject and the adjective together. Bu ağaçlar büyük literally means 'this trees big', which we naturally understand as 'these trees are big'.

Shouldn't the adjectives büyük and küçük also get a plural suffix because the trees and birds are plural?

No, adjectives in Turkish do not change to match plural nouns. They always stay in their base form when describing a subject. You just write büyük (big), not büyükler, even though the trees are plural.