Q: Copying Files to a New Laptop

If you’re using a network connection, start File Sharing, choose Connect to Server from the Finder’s Go menu, put in the other computer’s IP address, and copy the files.

If you’re using Target Disk mode, open the other computer’s internal drive, navigate to those files, and copy them over.

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Yes. How were you going to copy all your files? And, using what cable? It's difficult to offer a more complete answer when you don't provide the complete information - your might read Writing an effective Apple Support Communities question for help.

Start up the old computer with the T key held down, open its internal drive, double-click Users, and look inside the home folder.

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Sorry, not such intention. I have no way of knowing what you know when it isn't included by you. Sorry you misunderstood.

Once you are connected using TDM you can drag and drop files just as you would between any two disks. If you use Migration Assistant, then you will be transferring an entire user folder. If the files are in that folder, then they will be copied along with all the other files. Don't use MA if it isn't your desire to transfer the entire user account from the other computer. Be sure you are booting the old computer into TDM, not the new one. The old computer's disk drive will appear on the new computer's Desktop. Target Disk Mode for more information.

He did include the info in his original post:

iPHOTO LIBRARY

I bought the cable to copy files from my old laptop to my new.  I want to know if I can copy specific files, such as the iPhoto Library file.  Is this possible?