Learn Turkish: Giyiniyoruz ve diş fırçalıyoruz. - We are getting dressed and brushing our teeth.

In English, we say our teeth, but in Turkish, routine actions are often treated as general concepts. You just use the bare singular word diş (tooth). The phrase diş fırçalamak works like the single idea of tooth-brushing.

I know the verb giymek (to wear). Why use giyinmek here?

Giymek is used when you are putting on a specific item, like a hat or shirt. Giyinmek means the general action of getting dressed. The -in added to the verb shows it is an action you are doing to yourself.

Why is the spelling fırçalıyoruz instead of fırçalayoruz?

The dictionary form is fırçalamak (to brush). In the present continuous tense, when a verb root ends in a or e, that letter drops and is replaced by ı, i, u, or ü before the -yor suffix. Here, the a changes to ı to follow vowel harmony.

Do we need to put Biz (we) at the beginning of this sentence?

No, it is not required. The -uz ending on both giyiniyoruz and fırçalıyoruz already means we. You only need to add Biz if you want to put special emphasis on who is doing the action.