Learn Russian: Памятник на площади.

Because it describes a location after the word на, it must be in the Prepositional case. For feminine nouns that end in a soft sign (ь), like площадь, the soft sign changes to и in this case.

Since площадь ends in a soft sign, how do we know it is a feminine word?

Nouns ending in a soft sign (ь) can be either masculine or feminine, so you usually have to memorize their gender when you learn them. However, almost all Russian nouns ending in -адь, like площадь and тетрадь (notebook), are feminine.

Could I use в (in) instead of на (on) for a square?

No, Russian naturally uses на for open public spaces like squares, streets, and stadiums. You would use в for enclosed spaces or borders, like being inside a building, a room, or a city.