What if my base station is not an airport?

You can only "wirelessly extend" a wireless network created by an Apple AirPort Base Station.

Otherwise you can only create a "roaming network". That is a better idea anyway.

Exactly. That will work.

Give the AirPort network the exact same network name and security settings as your existing wireless network and you will have created a "roaming network". This is the ideal configuration for large areas that require multiple access points.

MirandaDuncan wrote:

And I can leave the original router/modem wireless and the airport won't try to create another network?

Yes.

Technically this does create another network, but one that appears to be completely identical and indistinguishable to the computers that use it. The result is that a laptop or wireless device can "roam" between the two wireless networks and they will switch seamlessly from one to another. You will see one and only one wireless network available. Given enough access points and Ethernet cable you can theoretically create a wireless "hotspot" as big as you want - within reason.

It's actually even better than that. All newer Apple base stations are dual band units. By default they actually create two wireless networks - one 2.4 GHz network for older computers and iOS devices, and one 5 GHz network for newer iPhones and iPads. These networks are also indistinguishable from one another and appear to be one network, for all practical purposes.

You can configure an AirPort wirelessly. A brand new, unconfigured AirPort base station creates an open wireless network called "Apple network nnnnnn". Connect to that one, use AirPort Utility to configure it, then connect to the wireless network you just created with it.