Setting up a wireless router on a Mac is a process not unlike setting up a router on a PC, but with a few alterations in the latter steps that require a knowledge of the layout of Mac OSX. With a wireless router and the wireless router manufacturer's provided documentation, a wireless network can be set up and a router hooked up to a modem and Mac in a relatively short period of time and with little hassle.
Make sure that the Mac is not currently connected to the internet via the ethernet line. Unplug the cable modem from the wall to start off with. Then, connect the wireless router to the cable modem. To do so, take the network cable that leads from the cable modem into the back of the Mac computer and plug it into the router port that is labeled either Internet, WAN, or WLAN (these listings may vary by individual router, but generally this rule should apply to the router you have in hand).
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Plug the cable modem back into the power socket and allow it to initialize. This will take a few seconds. Make sure the computer is turned on as well, so as to allow complete initialization. Create a temporary internet connection by running the wireless router network cable straight into one of the still available ports on the router. Make sure that this port is not the WLAN, WAN or Internet port mentioned above.
Open your browser. Locate the address bar and then type in and enter the special address that was provided by your router manufacturer though that device's documentation. Also enter a password if required (check your documentation).
Input the wireless network name, or SSID. This will be entered into the configuration page that pops up following your input of the password in the step above. The SSID is a name of your choosing. Also, consider password encrypting the network with a password of your choice. Then, "Apply" your settings.
Disconnect the network cable from your Mac so as to sever the temporary internet connection you established. This wired connection will no longer be necessary seeing as the wireless router is now configured. The wireless card contained within your Mac will do the work from now on.
Right click on the network icon, which is the set of waves in the upper right hand side of the Mac OSX. This will allow your Mac to connect to your new wireless router and the network you set up. After clicking on this wireless icon, select the SSID name of your network from the drop down list, wait a moment, and then enjoy browsing the internet free of wires.