The data dictionary (represented by class RDMFieldDictionary) is just a piece of data which you can download from the TREP server or you can load it from a local file. Thus, the data dictionary is not something you "connect to". Therefore I'm confused by your choice of words.
Secondly your question about how to execute something as a Windows service is very broad. You haven't specified which TREP API you're using, but I'm guessing it is one of the Java APIs (correct?). In this case the question is "how to run a Java application as a Windows service". This has nothing to do specifically with the API but relates to Java in general or even to Windows in general (java.exe is really just like any other executable on a Windows machine). You can Google for it. There are many, many solutions out there to address this problem. Many people (used to) use the so called Java Service Wrapper from Tanuki but since they changed their license it has become somewhat less popular. Anyway, there are many alternatives.
If this was not the answer you are looking for then perhaps you can elaborate a bit. You've asked a question where you've crammed everything into the title of the question. There's a lot of room for detailing your question.