Learn Russian: Нет, вчера было тринадцатое апреля. - No, yesterday was the thirteenth of April.

It is the neuter form of the ordinal number (a number that shows position, like first, second, thirteenth). When stating the date in Russian, we always use the neuter form because it grammatically agrees with the hidden neuter word число (date or number). You are essentially saying "the thirteenth [date]".

Why do we use the neuter past tense было here instead of был or была?

In the past tense, Russian verbs must match the gender of the subject. The subject here is the date, тринадцатое, which is neuter. Therefore, the verb "to be" must take the neuter past tense form было.

Why is April spelled апреля instead of апрель?

To say "of April", we put the month into the Genitive case. The word апрель is a masculine noun ending in a soft sign, so its Genitive ending is -я. This makes тринадцатое апреля literally mean "the thirteenth of April".

How do I pronounce the д in тринадцатое?

You don't! The д is completely silent. You should pronounce the word as if it were written "тринацатое". This dropping of the "д" sound happens in all Russian "teen" numbers and tens ending in -дцать.