copying them should be as simple as drag-n-drop after you get the two computers talking to each other. Getting them to network together can be the hard part.

on the photo folder and select Send To and move them that way. Or, click on copy and then paste it the folder where you want them on yor new computer.

right click copy and paste to a flash drive. You can do large folders easily. If you have a lot of little folders it might be time consuming.

If you have a mac I have no clue

you can run the following from the Start -> Run...
"fsquirt"

This is assuming both computers are not connected to a network.
If they are, then create a network share on the destination computer and map a drive letter from the source computer.