Локер открывается картой доступа.

Открывается is the verb открываться, which is the -ся form of открывать.

In this sentence, -ся gives the verb a passive-like meaning:

• Локер открывает... = The locker opens ... something, which does not make sense here.
• Локер открывается... = The locker opens / is opened ...

So the sentence means that the locker is opened by means of an access card.

Here -ся does not mean that the locker is literally doing the action to itself in the English reflexive sense. In sentences like this, it often makes the verb sound passive-like or middle voice:

• Дверь открывается ключом = The door opens / is opened with a key
• Локер открывается картой доступа = The locker opens / is opened with an access card

Russian often uses this structure where English might prefer is opened.

Because картой is the instrumental case of карта.

The instrumental case is commonly used for the tool, means, or instrument by which something is done:

• ключом = with a key
• ручкой = with a pen
• картой доступа = with an access card

So:

• карта = card
• картой = with a card / by card

Доступа is the genitive singular of доступ.

In Russian, one noun often modifies another by putting the second noun in the genitive:

• карта доступа = access card
• literally, card of access

This is a very common pattern:

• номер телефона = phone number
• центр города = city center
• бутылка воды = bottle of water

So картой доступа means with an access card.

It is present tense, imperfective.

But in Russian, the present tense is often used for:

• general facts
• habitual actions
• instructions
• how something works

So here it means something like:

• The locker opens with an access card
• The locker is opened with an access card
• This locker operates by access card

It is not mainly talking about one single future event.

It usually focuses on the method, not the person.

So the sentence tells you how access works: the locker is opened by using an access card. It does not strongly specify whether:

• the card unlocks it automatically,
• you tap/swipe the card,
• or a person uses the card to open it.

The important idea is simply: an access card is the means of opening it.

Локер is in the nominative singular.

It is the grammatical subject of the sentence:

• Локер = the locker
• открывается = opens / is opened
• картой доступа = with an access card

So the structure is: subject + verb + instrument

Локер is a loanword from English locker. It is used in Russian, especially in modern commercial, fitness, office, hotel, or storage contexts.

It is treated as a masculine noun:

• этот локер
• новый локер

In some situations, native speakers might also say шкафчик, depending on the kind of locker and the style of the text. But локер is understandable and natural in many modern contexts.

Yes. Russian word order is flexible, although the neutral order here is:

Локер открывается картой доступа.

That sounds like a plain, neutral statement.

Other orders are possible, but they change the emphasis:

• Картой доступа открывается локер.
  This emphasizes the access card.
• Открывается локер картой доступа.
  Possible, but less neutral and more context-dependent.

For a learner, the given order is the best default.

Yes.

• Локер открывается картой доступа.
• Локер открывается с помощью карты доступа.

Both mean roughly The locker is opened with an access card.

The difference:

• картой доступа is shorter and more direct
• с помощью карты доступа is a little more explicit: with the help of an access card

In many practical contexts, the shorter instrumental form is very natural.

A natural stress pattern is:

Ло́кер открыва́ется ка́ртой до́ступа.

Approximate pronunciation:

• Ло́кер = LOH-ker
• открыва́ется = at-kri-VA-yet-sa
• ка́ртой = KAR-tay
• до́ступа = DOS-too-pa

A few helpful notes:

• Unstressed о is usually pronounced closer to a
• -ся at the end is usually pronounced like -sa
• The stress matters a lot in Russian, so it is worth memorizing it with the word

A fairly literal translation is:

The locker opens with an access card.

A more natural English interpretation in many contexts is:

The locker is opened with an access card.

Both are good ways to understand the Russian sentence. Russian often uses this -ся construction where English may choose either an active-sounding form like opens or a passive form like is opened.