Answer:
You can do one of two things:
If both are recent, and both desktops, it would be easiest to simply swap the hard drive. You get TS2 and all of your other data.
IF they are many years apart, or are laptops, simply install the sims 2 on the new computer, copy the My Documents/EA Games/The Sims 2 folder from your old computer to the same place on your new computer, then uninstall from your old computer. Be sure to install TS2 first, then replace the folder in documents. Good Luck!