ifor said:
The AirPort Extreme in handling DHCP. I've been in terminal, but I can't work it out.
Not familiar myself with the Airport so can't help on that front I'm afraid...
As BMFDrums mentioned, another tact would be to connect the Pi to a tv (hdmi or phono type video connection). You'll also need to connect a keyboard temporarily.
Boot the Pi up and have a look out for the IP address being assigned (there'll be lots of info scrolling up the screen so just keep an eye out for it). If you do miss it, once the Pi has booted up and is at the command prompt, and type (without the quotes) "sudo ifconfig"
You should get something similar to the following in return:
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
inet6 addr: ::1/128 Scope:Host
UP LOOPBACK RUNNING MTU:65536 Metric:1
RX packets:16020 errors:0 dropped:0 overruns:0 frame:0
TX packets:16020 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:0
RX bytes:3166316 (3.0 MiB) TX bytes:3166316 (3.0 MiB)
wlan0 Link encap:Ethernet HWaddr c8:3a:35:c7:82:d2
inet addr:192.168.0.20 Bcast:192.168.0.255 Mask:255.255.255.0
inet6 addr: fe80::ca3a:35ff:fec7:82d2/64 Scope:Link
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:1583308 errors:0 dropped:0 overruns:0 frame:0
TX packets:455051 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:1448920983 (1.3 GiB) TX bytes:69529211 (66.3 MiB)
Ignore the first "Local Loopback" section... in the next section you should see your Pi's IP address (inet addr) - mine here is 192.168.0.20
Hope that helps...