Fortunately, there is a simple way to accomplish this using translation files.
- Navigate to app/locale/en_US folder (or whichever language you want to edit)
- Select and edit Mage_Checkout.csv.
look for something like this: %s was added to your shopping cart.,%s was added to your shopping cart.
Now, change the line after the comma to what you would like it to be:
%s was added to your shopping cart., You can translate it here!
- Save the file and clear the cache, you would notice it changed.