What occurs in the background when an application such as Skype is installed e.g. logs, synchronization, etc?
where is the application installed


The .apk file is put into /data/app (see: Where in the file system are applications installed?)


  where are its preferences stored


This depends on the application. If it uses the SharedPreferences classes then they go in /data/data/&lt;app's package name&gt;/shared_prefs, but they could feasibly be stored anywhere the app can write data to (i.e. all of /data/data/&lt;app's package name&gt;, the SD card, etc).


  where is information such as usernames and passwords stored


This also depends on the app. Most often, probably somewhere in /data/data/&lt;app's package name&gt;. They could also use AccountManager APIs (the app must request this permission) which I believe will use the /data/system/accounts.db database.