Normally, USB devices such as flash drives should auto-mount, though I don't use the Chrome OS per se (my normal operating systems are Red Hat Linux clones). In cases where they don't auto-mount, you can do this.
Before inserting the device in a USB port, look at the drives in /dev, as in "ls /dev/sd?"
Look at /dev/sd? again (after a few seconds to allow the system to detect it) to see the new device ID. IE, if before you had /dev/sda and /dev/sdb, then after you should see /dev/sdc.
Once the system has detected the device, you can mount it to an empty directory of your chosing, such as /mnt/usbdrive: sudo mount /dev/sdc1 /mnt/usbdrive
This last bit assumes that the device has a partition which would be seen as /dev/sdc1. You can tell with the command "ls /dev/sdc*', assuming that that device is detected as /dev/sdc. In any case, this would be pretty normal. Note the use of the "sudo" command - that allows you to run a command, such as "mount" as the system administrator (root) account.