There are really two questions to your question: how to use GATE to search for named objects and, possibly, how to insert GATE into your application.
Named recognition or classification of entities is a huge area of research, and depending on which named objects you want to find, different approaches may be most effective. GATE provides a very simple list of place names and a rule-based approach for finding certain categories of named objects in English text: ANNIE. If the categories ANNIE has found are interesting to you, one way to get started is to understand and improve what is already provided by ANNIE. The ANNIE pipeline will create annotations for Person, Organization, etc. In your document, and you will need to use or write a PR that accesses these annotations and does everything you need with the functions or text of these annotations. Take a look at the GATE manual http://gate.ac.uk/sale/tao/split.html he explains ANNIE, and also has some documentation on how to implement GATE (how to use GATE directly from your Java program without starting the GUI).