Извините, где касса самообслуживания?

• Извините: eez-vee-NEE-tye (stress on -ни-). The тe at the end is like tye.
• где: gdye (one syllable; the гд is a tight cluster).
• касса: KAS-sa (stress on the first syllable).
• самообслуживания: sa-ma-ab-sloo-ZHEE-va-nee-ya (common stress: -жи-).
  Tip: ж is like the s in measure.

Because Извините is used as a polite “attention-getter” (like Excuse me,), and Russian usually sets that off with a comma: Извините, …. In speech it’s a short pause before the actual question.

Both can mean Excuse me in this context.

• Извините is very common and neutral for getting someone’s attention in public (shops, streets).
• Простите can sound a bit more “I’m sorry / pardon me,” sometimes slightly more formal or more apologetic, but it’s also fine as “excuse me.” If you’re just asking for directions in a store, Извините is a safe default.

It’s in the nominative because где (“where”) usually asks for a location in a simple “X is where?” structure:
Где касса? = “Where is the cashier/checkout?”
Russian often omits есть/находится (“is/is located”), so the noun stays nominative.

самообслуживания is the genitive singular form of самообслуживание (“self-service”).
Russian frequently uses Noun + genitive to mean “Noun of X / X-type Noun”:

• касса самообслуживания = “self-checkout” (literally “checkout of self-service”)
• Compare: зал ожидания (“waiting hall”), комната отдыха (“rest room”).

касса is broader than English cash register. In stores it commonly means:

• the checkout counter/area, or
• the cash desk, i.e., where you pay. So in this sentence it naturally means self-checkout as a place/area, not the machine itself.

Yes. Use plural if you’re asking where the self-checkout stations are in general:

• Где кассы самообслуживания? = “Where are the self-checkouts?” Singular (Где касса…?) can still work even if there are several, especially if you mean “the self-checkout area.”

The natural phrase is касса самообслуживания.
самообслуживание касса is not idiomatic, and Где самообслуживание касса? is incorrect word order/structure.
You can vary the sentence slightly:

• Извините, где здесь касса самообслуживания? (very common; здесь = “here”)
• Подскажите, пожалуйста, где касса самообслуживания? (more polite: “Could you tell me…”)

где means where. It doesn’t require a preposition by itself. You typically just put the place noun after it:

• Где касса? Где туалет? Где выход?
  If you want to be more specific, you add extra words:
• Где здесь касса? (“Where is the checkout here?”)
• Где находится касса? (“Where is the checkout located?”)

It’s already polite because of Извините. Adding пожалуйста can make it even softer:

• Извините, пожалуйста, где касса самообслуживания?
  That’s very natural in a shop.

Common replies you might hear:

• Вон там. = “Over there.”
• Прямо и направо. = “Straight ahead and to the right.”
• У выхода. = “By the exit.”
• Рядом с обычными кассами. = “Next to the regular checkouts.”