Can I just plug an ethernet cable into it and my PC and access it?
Possibly. Without a router/dhcp server you'd need to do some things manually that are normally automatic.
1. Manually set a suitable IP address for the wired Ethernet connection on your PC
2. Connect your linkstation to the pc and power it on
3. Use nasnavigator to set the ip address of the linkstation to one on the same subnet as your PC
4. access it at that ip address
I don't think you need a cross-over cable since modern NICs handle that automatically, though I'm not certain about that.
You could also try connecting both to an old router even if it's not connected to the internet, the dhcp server would then setup ip addresses for both device for you.