Learn German: Wir feiern am ersten Mai. - We are celebrating on the first of May.

When you state a date using am (on the), the ordinal number acts like an adjective in the dative case. After am, ordinal numbers always get the ending -en. So, erste (first) becomes am ersten.

Why do we use am in front of the date?

The word am is a short form of an dem (on the). In German, you always use am to say something happens on a specific date or day of the week. Since months like Mai are masculine, the dative article is dem, which squishes together with an to make am.

Shouldn't ersten be capitalized because it means 'the first'?

No, it stays lowercase here. Ordinal numbers act like adjectives when they come right before a noun (in this case, the month Mai). Since it is a regular adjective describing the month, ersten is lowercase.

The translation says 'We are celebrating', but isn't feiern just present tense?

Yes! German doesn't have an '-ing' tense. Wir feiern translates to both 'we celebrate' and 'we are celebrating'. German also frequently uses the present tense to talk about firm future plans, so this is the natural way to say you plan to celebrate on May 1st.