Q: I'm having trouble connecting wifi to my iMac G5.

Providing some additional details may be relevant to solving the problem.  There are several models of iMac G5.  Here's a list of all iMac models.  Which specific model do you have?

http://www.everymac.com/systems/apple/imac/index-imac.html

Also, what version of Mac OS X does it run?  You can select About This Mac from the Apple menu to get details about your system.

You do not need an Apple Airport Base Station.  But settings on your wireless router does make a difference.  For example, the last iMac G5 model (from 2005) has only 802.11b and g wireless, not 802.11n (unless you use a third-party add-on).  Make sure your wireless router is not set for 802.11n only.

As a test, place the iMac close enough to your router so that you can connect it using an Ethernet cable.  Do you get an Internet connection?  If so, select Software Update from the Apple menu to confirm you are running the latest possible system version for your release of Mac OS X.  If there's an update, try the wireless connection again after applying update.

If it's just called "iMac G5," it's probably the first iMac G5 from 2004.  Its wireless (802.11b and g) was "optional," meaning the customer could configure it with wireless (or not) when purchased.  Are you sure it has built-in wireless?  Is AirPort listed as networking choice in System Preferences Network pane (sidebar).  If it's listed there, is AirPort turned ON?

Also, how do I find out what my router is set to?

If it's not an Apple base station (which uses AirPort Utility for settings), you'll need to refer to the router's documentation for how to change its settings (including things like name and passcode for your wireless network).  You may find that info online on the manufacturer (or service provider) web site.  Often, non-Apple routers use a web browser interface; you enter an address like http://10.0.0.1 in a browser window, and that accesses the router's settings screen.

If you are still having a problem with the Wi-Fi connection, does your wireless network name appear as a choice when you click the AirPort status symbol in the menu bar?

As a test, does your iMac have an Internet connection if you use an Ethernet cable to connect directly with the router?