It should work by default when connected, however you might reach this page with the same issue I had, where you where missing a few essential steps.
- Be sure that your PSP is set into USB mode: Settings -> USB connection
- Be sure the kernel module
usb-storage
is enabled, you can check withsudo modinfo usb-storage
and enable it withsudo modprobe usb-storage
- Reconnect your cable after trying any of the previous steps
- If it doesn't get automounted, run dmesg to find the device (on my local machine it's sdb as seen in the output) and mount it manually (prefered with your user access rights so you don't have to use sudo for file copy)