Get the program "SuperDuper". Do a search for it and it's free.
Mount the new HD in your system and the old HD in a USB enclosure.
At boot time, hold down the "option" key and select the external (original HD) to boot from.
After you boot up, run SuperDuper and copy the external HD to the new internal HD. It will create an exact replica of your original HD on the new internal, and make the new HD bootable.
You might have to (should) run the "Disk Utilities" program to format your new internal HD to the "Mac OS Extended (Journaled)" file system. It seems that 99% of the disks you buy are pre-formated for Windows, so be sure to check the "Options" in the Disk Utility to make the new drive MacOS bootable before you format it. If not, you will finish the SuperDuper copy and find out there is something not right about your new HD.
After you are done (about 2 or 3 hours), reboot normally.
Keep the external HD (original) around for awhile - a week or so - to confirm everything went okay, then you can reformat it and use it extra storage, time machine, or what ever.