Nos despedimos en la salida.

Because the verb is despedirse, which is a pronominal verb often used for saying goodbye.

With nosotros, the pronoun is nos, so:

• yo me despido
• tú te despides
• nosotros nos despedimos

In this sentence, nos can feel reciprocal: we said goodbye to each other.

It can mean either one.

For nosotros, the present and the preterite of despedirse have the same form:

• nos despedimos = we say goodbye
• nos despedimos = we said goodbye

So you need context to know which one is intended.

It is usually taught as a reflexive/pronominal verb, because it uses reflexive-style pronouns like me, te, se, nos.

But in a sentence like this, with a plural subject, it often has a reciprocal sense:

• Nos despedimos = We said goodbye to each other

So grammatically it behaves like a reflexive verb, but the meaning here is often more reciprocal than truly reflexive.

It literally means at the exit or at the way out.

So en la salida points to a place/location. It suggests the goodbye happened by the exit.

Depending on context, salida can sometimes relate to departure, but in a sentence like this, learners will usually understand it as the exit.

This is a very common question.

• en la salida focuses on location: at the exit
• a la salida often refers more to the moment of leaving or on the way out

So:

• Nos despedimos en la salida = We said goodbye at the exit
• Nos despedimos a la salida = We said goodbye when leaving / on the way out

Both can be possible, but they are not exactly the same.

Salida has several meanings depending on context, including:

• exit
• way out
• departure
• outing
• output or result in some technical contexts

Here, because of en la salida, the most natural interpretation is the exit or the departure area.

Because Spanish often omits subject pronouns when they are not needed.

The verb form despedimos already tells you the subject is we.

So:

• Nos despedimos en la salida = normal and natural
• Nosotros nos despedimos en la salida = also correct, but more emphatic

You would add nosotros only if you want contrast or emphasis.

Yes. Very often, despedirse is followed by de to show who you are saying goodbye to.

For example:

• Nos despedimos de Ana
• Nos despedimos de ellos

In your sentence, that part is simply not stated. The sentence just tells you that the goodbye happened en la salida.

Yes, salida is a feminine noun, so it takes la.

That is why you get:

• la salida

It comes from the verb salir, but here it is a noun meaning exit, departure, or way out.

Yes. Spanish word order is flexible.

These are all possible, depending on emphasis:

• Nos despedimos en la salida
• En la salida nos despedimos

The original version is a neutral, natural order. Moving en la salida to the front gives a little more emphasis to where it happened.

Yes, it would be similar.

• Nos despedimos en la salida = We said goodbye at the exit
• Nos dijimos adiós en la salida = We said goodbye to each other at the exit

The version with despedirse is very common and often sounds a bit more natural in many contexts. The version with decirse adiós is also correct, but slightly more explicit.

It is pronounced with the stress on di:

des-pe-DI-mos

The full sentence is roughly:

Nos des-pe-DI-mos en la sa-LI-da

The main stresses are in di and li.