Quick answer
hay
One word for “there is” and “there are”. It never changes, never takes a plural, and never takes an article after a number.
One form, always
Hay comes from haber and is frozen. Singular, plural, masculine, feminine — always hay.
Hay un problema.There is a problem.
Hay tres problemas.There are three problems.
¿Hay wifi?Is there wifi?
No hay nada.There is nothing.
hay or está?
Use hay to say something exists, está to say where a known thing is.
¿Hay un banco por aquí?Is there a bank around here? — any bank.
¿Dónde está el banco?Where is the bank? — that particular one.
In the past
Había for “there was/were”, hubo for a one-off event.
Había mucha gente.There were a lot of people.
Hubo un accidente.There was an accident.
Memory trick
If you can put “a” or a number in front of it in English, Spanish takes hay. If you would say “the”, it takes está.
Typical mistakes
Hay son tres sillas.
Hay tres sillas.
hay already contains the verb.
Hay el libro en la mesa.
El libro está en la mesa.
A known, definite thing takes estar.
Check yourself
___ dos cafeterías en mi calle.