Before we get on with the detailed discussion of star formation, let's think about the basics first. We see O stars in H II regions and so, there must be continual star formation in the MIlky Way galaxy.
Star formation can persist in the Milky Way galaxy for several billion more years.
They essentially never die. As noted above, stars form in gas clouds in the ISM in the disk of our galaxy and triggers are needed. Spiral arms somehow serve as triggers . This suggests that star formation occurs in or near spiral arms.