Open up your command prompt and change directory (cd command)to the directory that has your adb.exe file in it. On windows it is usually in:
C:\Users\USERNAME\AppData\Local\Android\sdk\platform-tools.
Then type in:
adb pull /data/data/com.package.name/databases/YourDatabaseName
If the application is not debuggable then you will need to try another option:
You can create a backup of the application and then extract the backup file.
To do this type in:
adb backup "-f /FileName.ab -noapk com.package.name"
This will create an Android backup file (.ab) in the base directory of you main drive.
To extract this file, download the Android Backup Extractor at this address:
https://sourceforge.net/projects/adbextractor/
Extract the Android Backup Extractor files and then put your .ab file in the Android Backup Extractor folder. The open a command prompt and cd to the Android Backup Extractor folder. The type in the command:
java -jar abe.jar unpack YourFile.ab YourFile.tar
You will now have a zipped file in the Android Backup Extractor folder. Extract this file and you will have the applications database in the extracted folder.
seanmcateer 