Стоит мне забыть проездной дома, как я сразу вспоминаю о нём у входа в метро.

This is a very common Russian pattern meaning as soon as..., the moment..., or it only takes ... for ... to happen.

So:

• Стоит мне забыть проездной дома, как... = As soon as I forget my travel pass at home, ... = The moment I leave my pass at home, ...

It does not mean it is worth for me to forget here.

A few similar examples:

• Стоит мне лечь спать, как телефон звонит.
  As soon as I go to bed, the phone rings.

• Стоит ему начать говорить, как все смеются.
  As soon as he starts talking, everyone laughs.

This construction often expresses something that happens regularly, annoyingly, or immediately.

Because in this construction, the person connected to the infinitive is put in the dative case.

So:

• Стоит мне забыть...
• literally something like It only takes for me to forget...

Russian often uses the dative with impersonal or semi-impersonal structures like this.

Compare:

• Мне нужно идти. = I need to go.
• Мне трудно понять. = It is hard for me to understand.
• Стоит мне забыть..., как... = As soon as I forget..., ...

So мне is grammatically normal here.

It is from стоить, not стоять.

Here стоить does not mean to cost in the usual money sense. In this structure it means something like:

• it only takes
• one has only to
• as soon as

So:

• Стоит мне забыть... = I only have to forget... = As soon as I forget...

It is unrelated to стоять = to stand.

Забыть is the perfective verb, meaning a single completed act: to forget, to leave behind by mistake.

That fits this sentence well, because it refers to the moment the forgetting happens:

• Стоит мне забыть... = As soon as I forget / leave behind...

If you used the imperfective забывать, it would sound wrong or at least very unnatural in this structure, because the construction points to a specific completed trigger.

So:

• забыть = one completed act of forgetting
• вспоминать / вспоминаю = remembering, becoming aware, recurring action

Because the sentence describes a habitual situation or a repeated pattern:

• whenever I forget the pass at home,
• I immediately remember it at the metro entrance.

Russian often uses the present tense to talk about things that happen regularly:

• ...как я сразу вспоминаю... = ...I immediately remember... = ...I always end up remembering...

The imperfective вспоминаю works well because it presents this as a repeated, typical reaction.

If the sentence were about one specific past event, you would expect different forms, for example:

• Стоило мне забыть проездной дома, как я сразу вспомнил о нём... = As soon as I forgot my pass at home, I immediately remembered it...

Проездной is short for проездной билет and means a travel pass, transit pass, or season ticket, depending on context.

In everyday Russian, people very often just say:

• проездной

instead of the full phrase.

So in this sentence it means something like:

• a metro/bus pass
• a public transport pass

Here дома is an adverb, meaning at home.

So:

• забыть проездной дома = to leave/forget the pass at home

This is a very common use:

• Я дома. = I’m at home.
• Оставил телефон дома. = I left my phone at home.

This дома is not functioning like in the house/building in a literal spatial sense. If you said в доме, that would mean in the house/building, which is more physical and less idiomatic here.

Because the verb вспоминать / вспомнить can be used with о + prepositional case when you mean to remember / think of someone or something.

So:

• вспоминаю о нём = I remember it / I think of it

Since проездной is masculine, the pronoun is:

• он → о нём

This is a very natural pattern:

• Я часто вспоминаю о детстве. = I often think about childhood.
• Вдруг вспомнил о ключах. = I suddenly remembered the keys.

In many contexts, Russian can also use a direct object with вспомнить:

• Я вспомнил ключи is much less natural than Я вспомнил о ключах in most situations.

With remembering that something exists / that you forgot something, о + prepositional is especially common.

Because Russian pronouns agree with the grammatical gender of the noun, not with whether it is a person.

• проездной is masculine
• so the pronoun is он
• after о, it becomes о нём

The same happens with many inanimate masculine nouns:

• паспорт → о нём
• телефон → о нём
• билет → о нём

So о нём here simply means about it.

No. Here как does not mean how.

In the pattern Стоит..., как..., the word как introduces the result that follows immediately:

• Стоит мне забыть проездной дома, как я сразу вспоминаю...

This whole pattern means:

• As soon as I forget my pass at home, I immediately remember it...

So here как is part of the fixed construction and works more like:

• and then
• when
• as soon as

depending on how you translate the whole sentence.

Сразу means right away, immediately, at once.

So:

• я сразу вспоминаю = I immediately remember = I remember right away

It emphasizes how quickly the remembering happens — of course, in an ironic way, because it happens too late.

Russian often places сразу before the verb, but word order can vary:

• Я сразу вспоминаю о нём.
• Я о нём сразу вспоминаю.

The meaning stays similar, though the emphasis shifts slightly.

У входа means by the entrance, near the entrance, or at the entrance.

So:

• у входа в метро = at the entrance to the metro = by the metro entrance

Breakdown:

• у
  • genitive = by / near
• вход = entrance
• входа = genitive singular
• в метро = to the metro / into the metro, depending on context

Here вход в метро is a fixed idea: the entrance to the metro.

Also, метро is indeclinable, so it stays метро.

Russian has no articles, so nouns appear without words like a or the.

Whether проездной means:

• a pass
• the pass
• my pass

depends on context.

In this sentence, English naturally uses my pass or the pass, because the speaker is talking about their own travel pass. Russian does not need a separate word for that if the context already makes it clear.

Yes, and that is probably the best way to understand it.

The present-tense forms suggest a repeated experience:

• Whenever I forget my pass at home, I immediately remember it at the metro entrance.

This is not mainly about one isolated incident. It describes a pattern that keeps happening.

That is why the sentence sounds a bit humorous or self-ironic.

Yes, Russian word order is flexible, but the original order sounds natural and expressive.

Original:

• Стоит мне забыть проездной дома, как я сразу вспоминаю о нём у входа в метро.

You could rearrange parts for emphasis, for example:

• Стоит мне дома забыть проездной, как я сразу вспоминаю о нём у входа в метро.
• Стоит мне забыть дома проездной, как я сразу о нём вспоминаю у входа в метро.

These are possible, but the original version is very natural.

Russian word order often helps show what is being highlighted:

• проездной дома keeps the forgotten item and place together naturally
• сразу before вспоминаю highlights immediacy
• у входа в метро leaves the punchline until the end

Yes. The sentence has a very natural ironic everyday-life tone.

The idea is:

• you forget the pass at home,
• and naturally you remember it only when it is already useless to remember — at the metro entrance.

So the structure and word choice create the feeling of:

• typical bad luck
• annoying habit
• of course I remember at the worst possible moment

That kind of nuance is very common in Russian with:

• Стоит..., как...
• сразу
• present tense for repeated situations