Hi There, since Acer do no release a wlan driver for Windows XP, you need to use the driver for Window Vista. If you do not have the driver for Windows Vista, you download it from here
. After finish downloading, then un-zip the file. Now let's start to install the wlan drivers. Go to your "Start Menu", then "Settings", "Control Panel" then "System", system properties windows will be pop up. Then select "Hardware" tab, and then click on "Device Manager" button. You will then see "Device Manager" windows. Look for your "Network Adapter" and you will see your wlan network adapter with red cross mark.Right click your red crossed wlan adapter, then select "Update Driver"
You will prompted with "Hardware Update Wizard" then select on "No, not this time" radio button and click on "Next" button. On next windows, select "Install from a list or specific location (Advanced)" radio button and then select "Next" buttons.
Then another window will pop up, then select "Don't search, I will choose the driver to install", then click on "Next" button. Then you will come to this windows "Select Network Adapter", you will see you existing network adapter that do not working, then select "Have Disk", and browse to the location where you have unzip the driver. Then Select the appropriate driver for your laptop. Acer Aspire laptop 4720z come in 3 wlan varian, Intel chipset, broadcom, and Atheros and I don't know which one is on your laptop. Just try one by one if you are not sure, it's only 3 to choose from.
Hope my solution could help you out.