First, an assumption on my part as you didn't tell us about certain aspects of your current configuration: I am assuming you have (or will want) broadband internet service (i.e., a cable modem, DSL, or satellite service) that currently connects via ethernet to your iMac.
The Airport Express has only one ethernet port on it, and that is where your broadband connection would go for wireless distribution to your two computers.
I don't know much about the availability of peripheral "slots" in the G3 iMacs, but if it has a PCMCIA (or Cardbus and PCCard are other names for it) like a laptop, then you could insert a standard laptop-type wireless card there. (Be sure it is Apple-compatible or maybe Apple has one for their laptop line?). If it doesn't take laptop-type cards, then you'll have to use a USB wireless client. I didn't see one on the Apple Store website, so you'll need to get another brand, making sure that it has appropriate Apple software available for the one you pick. The Airport Express uses industry-standard 802.11g wireless protocols, so any manufacturer's standard hardware will work but it will need Apple drivers rather than the more common Windoze stuff.
Then it is straightforward - follow the instructions in the Airport Express documentation.
I have an iMac G3 and I am purchasing an eMac G4. I want to put them both on a wirelees network and I've ordered the emac with the Airport Extreme card and the Airport express base. What would I need to hook the G3 up to the wireless network? I'm new at the wireless thing and unsure what is necessary. Thanks for the help.