"A szakács belép az ebédlőbe."

Translation: The cook steps into the dining room.

[vvsey]

The cook enters the dining room.

[KiritsuguZFC]

Is "belép" actually used as "to enter"? And is "lép" actually used? Because in English I can't think of many situations I would actually use "to step".

[vvsey]

Yes, and yes.
"To step" is "lépni". The noun version is "lépés".
"One step forward, two steps backward" - "Egy lépés előre, két lépés hátra"
"A small step for me..." - "Egy kis lépés nekem..."
"Please step forward" - "Kérlek, lépj előre"

To enter/join a group, to become a member, is also "belépni".

To just generally enter a building or other place is more generally "bemenni". But when you "make an entrance", that is, when it is a little bit more emphasized, you can say "belép".
Imagine a guided tour of some castle, and the guide says "As we enter the next room..." or "As we step into the next room..." - "Ahogy belépünk a következő szobába..."
You can also "lép" in chess. "I make a move" - "(Én) lépek".

[Krisbaudi]

This is a very good answer :-), thank you!

[piguy3]

Does ebédlő also mean "lunchroom," like in a school?

[vvsey]

Yes, very much so.