Learn Turkish: Antrenmanda önce selamlaşıyoruz. - We first greet each other at training.

It comes from the reciprocal suffix -ş. The base noun is selam (greeting), which becomes the verb selamlamak (to greet). Then we add the reciprocal suffix to make selamlaşmak (to greet each other). Because the verb stem selamla- ends in a vowel, we just add the consonant -ş instead of the full -ış or -iş.

The translation says "we greet", but selamlaşıyoruz has the continuous -ıyor ending. Why?

While -ıyor is the present continuous tense (literally "we are greeting each other"), Turkish frequently uses this tense for routines and habits. In English, we use the simple present ("we greet") for habits, but in Turkish, using -ıyor for regular activities like a routine at training is very common and natural.

Doesn't önce usually mean "before"?

Yes, when it is paired with a noun using the "from" case (like maçtan önce, "before the match"). But when önce stands completely alone as an adverb like it does in this sentence, it translates to "first" or "firstly" — meaning "before doing anything else."