Learn Russian: Твои синие очки там.

Твои is the plural form of the possessive pronoun "your" (when speaking to one person informally). It has to match the noun it belongs to, which is the plural word очки (glasses). If it were a single masculine object, you would use твой.

Why does the adjective синие end in -ие rather than the usual plural ending -ые?

The dictionary form of this word is синий (blue), which is a "soft-stem" adjective. While most adjectives take -ые in the plural (like красные for red), soft-stem adjectives take -ие.

Is the word очки always plural in Russian, just like "glasses" is in English?

Yes, exactly! Очки is a word that only exists in the plural form. Because it is plural, any adjective or pronoun describing it, like твои and синие, must also be in the nominative plural form.

I don't see a verb here. Why isn't there a word for "are"?

In Russian, the verb "to be" (am, is, are) is almost always dropped in the present tense. You literally just say "Your blue glasses there" (Твои синие очки там).