Para ir al ayuntamiento, hay que pedir cita previa.

Para + infinitive is a very common way to express purpose in Spanish: in order to go / to go.

So:

• Para ir al ayuntamiento = To go to the town hall / In order to go to the town hall

Spanish uses the infinitive (ir) here because it is not focusing on a specific conjugated subject like I go or you go. It is just stating the purpose in a general way.

Because a + el contracts to al in Spanish.

• ir a + el ayuntamiento → ir al ayuntamiento

This contraction is required. Spanish only has two contractions of this type:

• a + el = al
• de + el = del

So al ayuntamiento is simply the correct combined form of to the town hall.

In Spain, ayuntamiento usually refers to the town hall, city hall, or the municipal council/administration.

Depending on context, it can mean:

• the building where local government offices are
• the local government institution itself

In a sentence like this, it often suggests dealing with the local administration in an official or bureaucratic context.

Hay que + infinitive is a very common structure meaning:

• one must
• you have to
• it is necessary to

So:

• hay que pedir cita previa = you have to book/request an appointment first

Grammatically, this is an impersonal structure. It does not say who has the obligation specifically. It means that this is the general rule for anyone in that situation.

Because hay que gives a general, impersonal obligation, while tener que gives an obligation for a specific person.

Compare:

• Hay que pedir cita previa. = You have to / One has to book an appointment in advance.
  This is a general rule.

• Tienes que pedir cita previa. = You have to book an appointment in advance.
  This speaks directly to you.

In notices, instructions, and official information, Spanish very often uses hay que because it sounds general and neutral.

In Spain, pedir cita is the normal expression for requesting / booking / making an appointment.

Literally:

• pedir = to ask for / request
• cita = appointment

So pedir cita is the standard collocation. Even if English often says make an appointment, Spanish commonly says ask for/request an appointment.

With official services in Spain, cita previa is a very common fixed expression meaning a pre-arranged appointment required before going.

Because Spanish often omits the article in set expressions or when speaking in a general, procedural way.

So:

• hay que pedir cita previa sounds like a general instruction: you need to arrange prior appointment
• hay que pedir una cita previa is also possible, but it sounds a little more like referring to an appointment as a countable item

In official notices and administrative language, dropping the article is very common.

In Spanish, adjectives usually come after the noun, so cita previa is the normal order.

• cita previa = prior appointment / appointment in advance

Also, cita previa is a very common fixed administrative phrase in Spain.

You may sometimes see previa cita or con previa cita in very formal writing, but that is a different style and not the basic everyday pattern. For learners, cita previa is the form to remember.

The comma separates the introductory purpose phrase from the main statement:

• Para ir al ayuntamiento, = introductory idea
• hay que pedir cita previa. = main message

It helps readability and sounds natural in writing. In some short sentences, Spanish can omit this kind of comma, but here it is perfectly normal and clear.

Yes. Spanish word order is flexible. For example:

• Hay que pedir cita previa para ir al ayuntamiento.

This means the same thing. It simply puts the main obligation first and the purpose afterward.

The version you were given starts with Para ir al ayuntamiento to frame the situation first, which is very natural in instructions.