Learn Polish: Nowy pociąg jest szybszy niż stary autobus. - The new train is faster than the old bus.

The basic adjective for "fast" is szybki. When an adjective ends in -ki, we usually drop that ending before adding the comparative suffix. For a masculine noun like pociąg, we add -szy, making it szybszy.

Does szybszy change if I'm comparing feminine or neuter things?

Yes! Even in the comparative form, the adjective must match the gender of the noun it describes. Because pociąg (train) is masculine, we use szybszy. If we were describing a feminine noun it would be szybsza, and for a neuter noun it would be szybsze.

Why do we use niż for "than" here, and what case follows it?

niż is a very common way to say "than" in Polish. The great thing about niż is that the noun after it stays in the Nominative case (the basic dictionary form). That's why stary autobus doesn't change its endings. You could also use od for "than", but that requires using the Genitive case (od starego autobusu).

Are both pociąg and autobus masculine nouns?