How do I transfer Boot disk from External HDD to newly inserted SSD?

I'm trying to upgrade from my MacBook Pro's original HDD to a SSD. Right now my external HDD, which I installed OSX Mountain Lion on, has to be plugged in to boot. If I unplug it, I get a white screen with a flashing folder icon upon boot up.

I open disk utility and it shows my samsung SSD, which I just repartitioned to use Mac OS Extended (journaled)

EDIT I click finder and it shows under devices: "OSX" which is the name I gave my external HDD currently running OSX.. and "Samsung SSD." OSX has the standard folders on a mac.. Samsung SSD is blank.

How can I get OSX to boot from my SSD rather than the external HDD? Thanks!

Would doing this get it to do that?

It looks like Disk Utility is being extra cautious and not allowing you to unmount the boot drive to copy it. Assuming your copy of Disk Utility is running from the OSX external drive, you will have to power down and try booting into Recovery.

Normally, you press Command R to enter recovery but I haven't tested with no recovery partition on the internal drive, so you might instead boot holding option to see if the OS can find a recovery HD on the external drive.

If you partitioned both drives and have no viable recovery, you will have to use internet recovery or otherwise get a bootable OS that isn't the one you are attempting to copy.

Worst case, return the bootable drive to the inside of the Mac and run an OS installer to re-install the OS onto the SSD. That will make a proper Recovery HD partition that will allow you to boot and run Disk Utility without needing a bootable OS separate than the two drives you want to copy.