Entering into a squad is called enlistment!

入隊 can refer to enlisting in any group that ends with 隊 (squad), like the 軍隊 (military) or an 音楽隊 (marching band). These are indeed the most common uses.

This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.