Hello, Ian,
I hope you've updated to OS X El Capitan and hope not you have any worries, regarding Wi Fi.
If not, keep on reading...
Actually, I too had this issue and I use a Wi Fi DataCard. First, I needed to connect he DataCard via USB to my MacBook Air (India) in order to use it, like Ethernet connection. I used to try plugging the DataCard into Wall through the provided Pin and was never able to connect to Internet, as in System Preferences>Network>Wi Fi, it always told, Wi Fi has the Self-assigned IP Address x.x.x.x and cannot access the Internet.
I was just unhappy and googled for solution, didn't get any fruitful blog which told me how to do what I want.
This is what I did to get the task done and now I can use Internet via Wi Fi, without connecting it to Mac directly:
1. You should be having a Mobile, probably, iPhone as I do. Make sure you've connected your Mobile to that Wi Fi network.
2. On your Mobile, go to Wi Fi Settings and connect to Wi Fi and tap the 'i' key or whatever to view the IP Address. It should start with 192.x.x.x.
3. Go to Mac, open System Preferences>Network>Wi Fi. Go to Advanced. Go to TCP/IP.
There you find Configure IPv4 and it should be set to Using DHCP. Select it, from the dropdown list, choose, Manually.
4. Then, you'll get a permission to edit IP Address, Subnet Mask and Router. Enter the information of Wi Fi, as on your Mobile, like IP Address and Router. Note that, you must enter the IP Address correctly, in the last part of IP Address, enter only the first digit.
Eg., my IP Address is 192.168.1.105. Just enter 192.168.1.1.
Enter Subnet Mask and Router without any changes.
5. Now, go to Hardware, in the same page, check if Configure is set to Automatically or not. If not set, set it to Automatically.
6. Go to DNS and press '+' symbol in bottom and add the DNS as found in your Mobile Phone's Wi Fi information Page. Note that, the DNS is as same as your Router.
7. Come back to DCP/IP and click Renew DHCP Lease and after that, change Configure IPv4 back to Automatically and Renew DHCP Lease again.
8. Click OK and then click Apply.
9. Try to connecting your Mac to Wi Fi. If not able to connect, go to step 4, where I told to enter only the first digit of last part of your IP. Enter the complete IP Address. Click OK and Apply. Forget not to set Manually back to Automatically and Renew DHCP License.
10. Try once again and this time, it should work.
P.S., I don't use Apple AirPort.
Now, I'm able to connect to Wi Fi network and this saves a lot of Battery.
Good Luck,
Niteesh.