The 2 months extension is automatic, you just need to tell them that you're using it by attaching a statement to the return, as Pete Becker mentioned in the comments.
From the IRS pub 54:
How to get the extension. To use this automatic 2-month extension, you must attach a statement to your return explaining which of the two situations listed earlier qualified you for the extension.
The "regular" 6 months extension though is granted automatically, upon request, so if you cannot make it by June deadline you should file the form 4868 to request a further extension.
Automatic 6-month extension. If you are not able to file your return by the due date, you generally can get an automatic 6-month extension of time to file (but not of time to pay). To get this automatic extension, you must file a paper Form 4868 or use IRS e-file (electronic filing). For more information about filing electronically, see E-file options , later.
Keep in mind that the due date is still April 15th (18th this year), so the 6-month extension pushes it back to October.
Previous 2-month extension. If you cannot file your return within the automatic 2-month extension period, you generally can get an additional 4 months to file your return, for a total of 6 months. The 2-month period and the 6-month period start at the same time. You have to request the additional 4 months by the new due date allowed by the 2-month extension.
You can ask an additional 2 months extension (this is no longer automatic) to push it further to December. See the publication.
These are extension to file, not to pay. With the form 4868 you're also expected to submit a payment that will cover your tax liability (at least in the ballpark).
The interest is pretty low (less than 1% right now), but there's also a penalty which may be pretty substantial if you don't pay enough by the due date. See the IRS tax topic 301. There are "safe harbor" rules to avoid the penalty.