Add a WebService to your code.
Add a insert & update trigger to your table.
Create a CLR function that you can call from the trigger.
In that CLR function, call the webservice with all necessary data.
In the webservice, do whatever you need to do based on the passed parameters.
Add a configuration table, and enter the webservice URL.
Pass the url as argument to your CLR function.
You should call the webservice asynchronously, so the delay is minimized.
Note:
I think it's also possible to call a web-service from pure SQL, so there's not necessarely a need for the CLR.