Аварийный выход ведёт к месту сбора.

Because аварийный agrees with выход.

• выход = exit
• It is masculine, singular, and here it is in the nominative case
• So the adjective must also be masculine singular nominative: аварийный

This is standard adjective-noun agreement in Russian.

Выход is in the nominative case because it is the subject of the sentence.

The basic structure is:

• Аварийный выход = the emergency exit
• ведёт = leads
• к месту сбора = to the assembly point

So literally, the emergency exit leads to the assembly point.

Ведёт is the 3rd person singular present tense of the verb вести = to lead.

So:

• я веду = I lead
• ты ведёшь = you lead
• он / она / оно ведёт = he / she / it leads

Here the subject is аварийный выход, which is singular, so Russian uses ведёт = leads.

A useful thing to notice: the dictionary form is вести, but the present-tense forms change quite a bit.

The correct form is ведёт, with ё.

In normal Russian writing, people often replace ё with е, so you may also see ведет. But the pronunciation is still ведёт, and the stress stays there.

That matters because:

• ё is always stressed
• it tells you the word is pronounced differently from е

For learners, it is very helpful to think of this word as ведёт.

Because the preposition к takes the dative case.

• dictionary form: место = place
• dative singular: месту

So:

• к месту = to the place

This is a very common pattern:

• к дому = to the house
• к столу = to the table
• к месту = to the place

So after к, you should expect the noun to change form.

Because место сбора means literally place of gathering/assembly, and after место Russian normally uses the genitive case to show what kind of place it is.

• сбор = gathering, assembly
• genitive singular: сбора

So:

• место сбора = assembly point / gathering place

This is a very common Russian pattern:

• чашка чая = a cup of tea
• центр города = the city center
• место сбора = place of assembly

Both can exist in Russian, but they are not exactly the same.

• к месту сбора = toward / to the assembly point
• на место сбора = onto / to the assembly area itself, often with more emphasis on arriving at the location

With вести, Russian often uses к to mean lead to / lead toward:

• Дорога ведёт к реке = The road leads to the river
• Лестница ведёт к выходу = The stairs lead to the exit

So ведёт к месту сбора sounds very natural.

Yes, it is a normal and understandable phrase. In safety contexts, you may also see:

• пункт сбора
• место сбора
• sometimes more specific expressions depending on the sign or institution

So место сбора is a good, standard phrase here.

The neutral word order is exactly what you see:

• Аварийный выход ведёт к месту сбора.

Russian word order is more flexible than English, so other orders are possible, but they would usually change the emphasis.

For example:

• К месту сбора ведёт аварийный выход.
  This puts more focus on where it leads

But for a normal sign or plain statement, the original order is the most straightforward.

A helpful stress-marked version is:

авари́йный вы́ход ведёт к ме́сту сбо́ра

Approximate pronunciation:

• авари́йный = a-va-REEY-ny
• вы́ход = VY-khat / VY-həd
• ведёт = vee-DYOT
• к ме́сту = k MYES-tu
• сбо́ра = SBO-ra

A few useful notes:

• ё in ведёт is always stressed
• final voiced consonants often devoice in pronunciation, so выход does not sound exactly like it is spelled
• the preposition к is unstressed and attaches closely to the next word

Russian has no articles like the or a/an.

So Аварийный выход can mean:

• the emergency exit
• an emergency exit

Which one sounds best in English depends on the context. On a sign or in a building description, the emergency exit is usually the most natural translation.

That is normal in Russian: context tells you whether something is definite or indefinite.