Amint megérkezik a villamos, átszállok rá, és azonnal indulok tovább.

Here amint means as soon as or the moment.

It is stronger than amikor, which usually just means when.
So:

• Amikor megérkezik a villamos... = When the tram arrives...
• Amint megérkezik a villamos... = As soon as the tram arrives...

In this sentence, amint fits well because the next actions happen immediately after the tram arrives.

Hungarian often uses the present tense for future events when the time is already clear from context.

Here, the sequence is obviously future because of amint and the overall meaning:

• first the tram arrives,
• then I transfer,
• then I continue.

So Hungarian does not need a separate future marker here. This is very natural. Using fog forms would usually sound heavier or less natural in a sentence like this.

Megérkezik means arrives.

The base verb is érkezik = arrive. The prefix meg- often adds a sense of reaching a result or endpoint, so megérkezik suggests that the arrival is completed.

In everyday Hungarian, megérkezik is a very common way to say arrive. It focuses on the fact that the tram has actually gotten there.

A is the definite article, so a villamos means the tram.

Hungarian uses definite articles much like English does. Here it refers to a specific tram the speaker is waiting for or expecting, so a villamos is natural.

Also, villamos by itself means tram or streetcar as a noun.

Átszállok means I transfer or I change to another vehicle.

This is different from felszállok, which means I get on / board.

So:

• felszállok a villamosra = I get on the tram
• átszállok a villamosra = I transfer to the tram

The prefix át- gives the idea of moving over from one thing to another.

Because átszállni normally tells you what you transfer onto / to.

The full form would be:

• átszállok a villamosra = I transfer to the tram

Once a villamos has already been mentioned, Hungarian replaces a villamosra with rá, which means roughly onto it / to it.

So:

• átszállok rá = I transfer onto it / to it

This is very normal Hungarian usage.

Rá is the short pronoun form that corresponds to -ra / -re, the ending used with this verb.

So:

• a villamosra → rá

This is the usual form when you mean onto it.

Why not bele? Because with vehicles like villamos, Hungarian commonly uses -ra/-re for getting on or transferring onto them:

• felszállok a buszra
• felszállok a vonatra
• átszállok a villamosra

So the pronoun also follows that pattern: rá.

Arra is possible only if you want extra emphasis, like onto that one specifically. In neutral speech, rá is the normal choice.

Yes, they can move.

In a neutral statement, Hungarian verbal prefixes usually stand directly before the verb:

• megérkezik
• átszállok

But if there is negation, strong focus, or certain other sentence patterns, the prefix can move after the verb:

• nem szállok át rá = I am not transferring onto it
• mikor szállsz át rá? = when are you transferring onto it?

So the prefix is not permanently glued in front of the verb in every situation, even though dictionary forms often show it that way.

Azonnal means immediately, right away, or at once.

It emphasizes that the speaker does not wait after transferring. The action continues without delay:

• és azonnal indulok tovább = and I immediately continue on

Its position before the verb is very natural in a neutral sentence.

Indulok means I leave, I set off, or I start moving.
Tovább means further, onward, or on.

Together, indulok tovább means something like:

• I continue on
• I set off again
• I go on from there

Using both words gives a more natural sense of continuing the journey after the transfer.
If you only said indulok, that would just mean I leave/set off.
If you said megyek tovább, that would also work, but it would feel a bit more like I keep going, while indulok tovább highlights the moment of setting off again.

There are commas because the sentence contains both a subordinate clause and coordinated main clauses.

Structure:

• Amint megérkezik a villamos, = subordinate clause
• átszállok rá, = main clause
• és azonnal indulok tovább. = another main clause joined with és

So:

1. a comma separates the amint clause from the main clause,
2. another comma appears before és because it connects two full clauses with finite verbs.

This punctuation is standard in Hungarian.