"June is a beautiful month."
Translation:A június szép hónap.
It feels a tiny bit more natural to me with the "a". Especially when talking about a specific June.
I sense a definite difference from English here. In English, you would rarely use "the" here, if ever. In Hungarian it is normal.
You can also do something like this:
"Június az egy szép hónap ". - literally "June, that is a beautiful month".
This is quite a common construction.
Van and vannak are left out if you talk about a property of the subject. In this example you're identifying "June" with "being beautiful".
You do use van and vannak if you're talking about conditions, most importantly timeframe and place. For instance: "Júniusban van sok szép nap." - "There are many beautiful days in June." It's not about June itself anymore, but June is the external frame given while talking about where/when those days are.