Do a Time Machine backup of the old machine to your external drive. Connect the drive to your new computer. If it's brand new and you're setting it up for the first time, then just follow the prompts and it will import everything from Time Machine.
Otherwise just run the Migration Assitant App (in the Utilities folder inside the Applications folder) on the new machine. This has worked really well for me on my last two upgrades. Moved everything, all my files, programs, settings, even the arrangement of icons on the desktop. And it is smart enough to know which system files to move from the old machine and which system files to leave alone on the new machine. 😉