Trademark registers are publicly accessible and searchable through each IP office's online database. To monitor for new applications that could infringe on your mark, search regularly for applications in your registered classes and territories that are identical or confusingly similar to your mark.
How frequently you perform searches matters a lot too. In most jurisdictions, you should at least do monthly searches. For US marks, the 30-day opposition window requires weekly or bi-weekly searches.
A trademark monitoring service automates this for you, scanning registers on a set schedule and alerting you of potential conflicts.