I assume you fit the HDD to the enclosure connect it to the router and it should be visible to all networked PCs
Thats correct.....when you connect it to the router, it will assign it an IP address automatically using DHCP.
I've not really used networked enclosures, as I run a server environment in my house, therefore I simply share the hard drives/partitions that I need. If the enclosure comes with software, then it will no doubt allow you to assign it an IP address.
If it doesn't come with software, then you can always access your router and it will have the option to view all DHCP clients.
To access the files on, you go to Start
In the run command, type \\XXX.XXX.X.X where the X's represent the IP address
and it will show you all the files/folders on the drive.
Alternatively, you can create shortcuts to the folder(s) you want in My Network Places.
Give me a shout if you need any further assistance.