clone and boot from segment I have an external hard drive with a case. It is an older computer’s hard drive. To use certain software, I have to boot from that hard drive but since I am running the computer from an external hard drive with a usb cable, it runs pretty slow. 


Mac has 500 GB drive ??? available
USB is OS X 10.6.8 and 500 GB drive with 240 available (260 GB space filled)


I’d like to transfer it to a section of my hard drive and have the option off booting from that section/drive. Do you know of tutorials that can tell me how to do this or do you know how?
What you are trying to do is called dual booting and your "segment" is actually what is referred to as a "disk partition" or just "partition." This is nothing more than a logical segmenting of the disk. While the data is all on one drive the operating systems will see it as two (logical) drives.

I have not done a Dual boot Mac in a long time so take this (overview) with a grain of salt and do some googling on dual booting your Mac with two Mac OS partitions (there will be a lot with Windows and Linux, ignore those).

Basically you would boot into recovery mode (COMMAND-R) at startup and go into Disk Utility. In Disk utility you should have the option of re-sizing your main Mac partition by clicking on it and dragging up to make it shorter. It will only allow you to resize the partition by removing unused space. How much you will be able to resize depends on how big your drive is and how much of it is used.

Once you have done that you should be able to create a second partition. Once that is done you can boot from your install media and point the installer to your new partition. Once that is done you can use the Apple Migration Assistant to move selected files/apps to the new partition from your old external drive.

Again this is a 30 mile view. No doubt others have more recent experience with this and can add to (and correct) the basic procedure here. But it is basically possible but like bmike mentioned knowing the relative sizes of your drives and available space will help...