Learn Polish: Metal jest cięższy niż kamień.

When you make a comparison using niż (than), the second thing being compared takes the exact same case as the first thing. Since metal is the subject and in the nominative case, kamień is also in the nominative case.

How do we get cięższy from the basic adjective ciężki (heavy)?

For many adjectives ending in -ki, -ek, or -ok, you drop that ending before making it comparative. So, we drop -ki from ciężki and add the comparative ending -szy to get cięższy.

Why does the comparative adjective end in -szy instead of -sza or -sze?

Even in their comparative forms, adjectives still have to match the gender of the noun they describe. Because metal is a masculine noun, we use the masculine ending -szy. If we were comparing feminine nouns, we would use -sza.

Could I use od instead of niż to say this?

Yes! But remember that od forces the next word into the genitive case. So if you use od, the sentence changes to: Metal jest cięższy od kamienia.