1) Back the files up to a thumb/flash drive (Highlight all your clients, Ctrl+B, then select the flash drive location.

2) "Sneaker net" that flash drive to the new computer.  Note the letter/location assigned to the flash drive.

3) Restore from the flash drive (Ctrl+R, group all).

Two observations:

*I always scan the flash drive for viruses/issues EVEN when moving between my own computers.

*Backing up your client data files *should* be a regular part of your daily routine (I often back up twice a day during filing season)