Learn Turkish: Bugün evdeyiz, parfüm sıkmamıza gerek yok. - We are at home today, we don't need to spray perfume.

It breaks down as sık-ma-mız-a: the verb root sık (spray), the verbal noun suffix -ma (spraying), the possessive suffix -mız (our), and the dative case -a (to). You need the dative -a here because the phrase gerek yok always requires it. Literally, the structure means "There is no need to our spraying perfume."

The translation says "we don't need to," but where is the "we" in the second half of the sentence?

The "we" is expressed entirely by the possessive suffix -mız inside sıkmamıza (our spraying). Since gerek yok literally just means "need does not exist," Turkish tells you who doesn't have the need by attaching a possessive ending to the action itself: "there is no need to our doing it."

I've seen the verb sıkmak used to mean "to squeeze" or "to bore someone". How does it mean "to spray" here?

Sıkmak is a very versatile verb! In addition to squeezing or boring someone, it is the standard verb used for dispensing liquids under pressure, like spraying a hose, applying deodorant, or even squeezing out toothpaste. In Turkish, you don't "wear" or "put on" perfume; you always "spray" it (parfüm sıkmak).

Let's review evdeyiz. Why is there a -y- in the middle of it?