Policing your trademark is an important task for maintaining the strength of your trademark rights. There are passive and active approaches:
Waiting until instances of confusion arise between your brand and that of a third party. Periodically searching the Internet and industry for potentially infringing brands.
If your trademark has real value, you'll want to proactively monitor the U.S. Patent & Trademark Office trademark application filings to determine if anyone is seeking rights to a confusingly similar brand. It is difficult for even the most experienced trademark attorneys to do this manually because one must look not just for "identical" trademarks, but those with:
phonetic similarity; orthographic similarity and misspellings; prefix, infix and suffix variations; vowel and consonant similarity; plurals and stemming; abbreviations and acronyms; and other similarities
Well-informed brand owners and intellectual property practitioners set up sophisticated trademark watch services for an annual fee. Every 1-2 weeks, the monitor queries trademark databases in the U.S., Europe and in other countries for newly filed applications that could infringe the trademark owner's rights.