How can I connect my PowerBook to the net - wirelessly

Unless yours is the original Powerbook G4 12"

http://support.apple.com/specs/powerbook/PowerBookG412-inch.html

These all had built-in wireless:
http://support.apple.com/specs/powerbook/PowerBookG4_12-inch_133GHz.html

http://support.apple.com/specs/powerbook/PowerBookG4_12-inch_15GHz.html

Not all eMacs are Airport Extreme compatible.

This one is not:

http://support.apple.com/specs/emac/eMac.html

and needs the original Apple Airport Card, which Apple no longer sells. In the U.S. there are several stores which offer it, but none that I can find ship to the UK. It may be available from eBay, though with the amount of fraud I've seen reported on eBay, you should be especially cautious trying to buy it.

This one is Airport Extreme compatible:

http://support.apple.com/specs/emac/eMacATIGraphics.html

Airport Extreme Base Station is compatible with both original Airport Card and Extreme Cards. Their configuration needs to be set for 802.11b/g if the eMac in question needs an original airport card. Also an Airport Extreme base station offers a LAN port which you could hook your eMac to if it is not compatible with the Airport Extreme Card. The Base Station's WAN port regardless of how you hook your eMac would then be hooked up to your broadband connection hardware.

So just to be clear, I need an Airport Extreme base station, and should use its LAN port to connect to my eMac (doing this replaces the need to hunt down an original airport card, right?). Do I need to buy this LAN cable or will it come with the Base Station?

You need to buy the LAN cable, and yes it replaces the need to hunt down the airport card. Cat-5 or Cat-6 ethernet cable should be fine.

Then the Base Station's WAN port connects to the broadband connection hardware on my wall at home. Then I'm done.
Sound right to you?

Yes. Just remember use the Airport Admin Utility to put in any settings you currently have in your Apple menu -> System Preferences -> Network so the Airport Base Station can manage the cable connection. Plus, make sure both machines have Apple menu -> System Preferences -> Network set for DHCP, and PPPoE is turned off.