Some of the answers aren't quite correct. Services (Android Service component) are NOT made to run in the background, they run in the default UI thread.
In all honesty, the question shouldn't be service or thread or anything. Your library does NOT need to kick start a service, it could simply be a class (singleton/static, whatever it is) that should extend AsyncTask (or anything else running in the background that I'll explain in a bit) and use the doInBackground method to send stuff to the server. Note AsyncTask is nothing but a Thread internally. So here's what I would do:
Let's call your library's main class that interfaces with your server ServerHelper. You can make this a singleton (or static but that's a separate discussion). Within this class create an innerclass say ServerHelperCommandTask and extend AsyncTask. You really should review AsyncTask in detail to understand how that works. Because you would be asked to override doInBackGround. Anything you put in this method will autmoatically get exectued in a separate thread off the UI. Then a callback is invoked called onPostExecute that you can override as you will get the result from doInBackground here. This OnPostExecute is called in the mainThread so you can check for say error results here, etc etc.
This would be the simplest method; however, there are many other methods and libraries that help you with networking and deal with all the background stuff internally. Google just release a library called Volley which you may be able to plugin and use as it would do all the parallel processing for you. But that may take a bit of learning curve. Hope you understand AsyncTasks as in your case if the data pushed isn't a lot, then AsyncTasks is the way to go. Also note that you can call multiple AsyncTasks but while that seems on the surface that it is kicking off multiple parallel threads, that isn't quite accurate since honeycomb as internally you can call 5 Asynctasks but all 5 of those tasks will be executed sequentially so you wouldn't have to worry much about serializing.