Radar, you can post your internal ip address(es) if you like, as long as they start with 192.168 they are "private" addresses that anyone can use internally. So nobody will be able to hack you because you post them. You could also just post the last set of digits for each device, since that is all that is really interesting. Just don't post the outside public ip address that you get from something like whatismyip etc.
Assuming your router is a typical consumer model you probably are using the 192.168.1.0 (or 192.168.2.x or 192.168.100.x etc) subnet. Your router should be 192.168.1.1 and your clients (computer, azbox, whatever) might start at 192.168.1.100 or maybe just 192.168.1.2.
If your clients start at 192.168.1.100 (your pc's last digits being .100 or .101 etc) I would suggest picking a static ip address below 100 since there is no chance the router will try to hand out that address since the router starts at 100 and goes UP. If your clients are getting low addresses like .2 or .10 etc then you could pick a high number your router wouldn't ever reach like .60 or something.
So you could end up with something like this:
192.168.1.1 router
192.168.1.30 azbox
192.168.1.100 1st client (via the "DHCP" dynamic numbering)
192.168.1.101 2nd client
etc..
I just picked .30 arbitrarily. You could go with 42 if you like Douglas Adams or whatever means something to you and you can remember it.
Or you can let the router hand them out and just check the screen on the Azbox to see what the address is. I'm with Lak7 though, you should just assign a static ip to the Azbox so you *always* know where it is at on your network and you don't have to fiddle.
If you don't want to post ip details, feel free to PM me if you have troubles and I'll help you out as well if you have trouble. Lak7's instructions should do it, I just wanted to point out it is best to pick a static ip that isn't within the range the router would hand out.