SOAP? REST? Something else?
Did you write the web service?
You can do a lot with Insert From URL Script step.
Or use CURL functions in MBS Plugin (or other plugins)
As Christian indicates: integrating with a web service is fairly standard. But it depends on what the web service expects.
You'll need to let us know what web service you are trying to connect to and what is not working before we can help you...
It is possible. If the web service needs SOAP, take a look at SOAP web protocol and FileMaker | FileMaker. If they use REST, take a look at Support for HTTP POST operations in FileMaker Pro | FileMaker.
If you're needing to use Rest with JSON, I can share some of my custom functions that help import from JSON and export into JSON.
Please see the Discussion "FileMaker for Fun". There's a script in the downloadable file, "<Create Chunks from Image>", that won't work for you, but will show I how I scripted the integration of my own web service with FM.