Without an article, lunedì means "on Monday" this week; with one, il lunedì means "on Mondays", every week. Months take a or in, and a date is il plus the plain number - il cinque maggio. Days and months are lower case.
Examples
- Ho lezione mercoledì.
- I have a class on Wednesday.
- Il sabato non lavoro.
- On Saturdays I don't work.
- Il mio compleanno è l'otto aprile.
- My birthday is on the eighth of April.
The mistake to avoid
Only the first of the month is an ordinal: il primo maggio, but il due maggio.
Where this fits in
Numbers, days, time, Italian A1: Count, talk about days and months, give the time, and handle numbers in real situations.