Learn Swedish: Smycket som du tittar på är inte äkta silver. - The piece of jewelry that you are looking at is not genuine silver.

In Swedish relative clauses, if the verb uses a preposition (like tittar på for "looking at"), the preposition stays at the end of the clause. Unlike in formal English where you might say "the jewelry at which you are looking", Swedish requires you to leave the preposition at the end. You cannot put på before som.

Can I skip the word som here, just like we sometimes drop "that" in English?

Yes! Because som is acting as the object of the relative clause (you are looking at it), you can drop it. It is perfectly natural and common to say Smycket du tittar på är inte äkta silver in everyday Swedish.

Why doesn't the adjective äkta get a T added to the end to match the ett-word silver?

The word äkta (genuine or real) is an invariable adjective. Because its base form already ends in an -a, it never changes. It stays exactly the same whether it describes an en-word, an ett-word, or a plural noun.

How can I tell from this sentence that smycke is an ett-word?

You can tell by the -t at the end of smycket! The base word is ett smycke (a piece of jewelry). Because the base noun already ends in a vowel, you just add -t to make it definite ("the piece of jewelry").