Install Sqlite
Open DDMS : Tools > Android > Android Device Monitor
Click on your device on the left.
You should see your application:
Go to File Explorer(one of the tabs on the right), go to /data/data/databases and select your application package
Ex: check image

Select the database by just clicking on it.
Go to the top right corner of the Android Device Monitor window.
Click on the pull a file from the device button:

A window will open asking you where you want to save your database file.Save it anywhere you want on your PC.
Now, open the SQLiteBrowser you installed. Click on open database, navigate to the location you saved the database file, and open.You can now view the contents of your database.