Learn Russian: Девятого мая на площади флаги. - On the ninth of May there are flags on the square.

To say that an event happens on a specific date, Russian puts the ordinal number (the day) into the Genitive case. Since days of the month are treated as neuter words, the nominative девятое (the ninth) becomes the genitive девятого (on the ninth).

Why is the month мая also in the Genitive case?

In Russian dates, you are literally saying the day of a certain month. This of relationship requires the Genitive case, so the nominative май becomes мая.

Why does площадь end in -и in the phrase на площади?

Площадь (square) is a feminine noun that ends in a soft sign. To show location (on the square), we use the Prepositional case with the preposition на. For feminine nouns ending in a soft sign, the Prepositional ending is always -и.

Where is the verb for there are in this sentence?

In Russian, the present tense of the verb to be is almost always omitted. The sentence literally reads On the ninth of May on the square flags, and the there are is naturally understood from the context.