You need to make changes in both your Parallels' VM settings and in System Preference's Sharing Pane.
First, in System Preference's Sharing Pane go to the Internet tab. Click the Stop button if Internet Sharing is already running, then select the connection you are sharing from (either Airport or Ethernet, depending on how you are connected to the Internet) and then select the Parallels virtual adapter (it's en2 on my MacBook), finally click on Start. You can now close System Preferences.
Second, open Parallels. In the VM configuration screen click the Edit button. In the Configuration Editor click on Network Adapter and then select the button next to host-only networking.
You should now be able to use the Internet from within Parallels.
This will not allow anyone else on the network to connect to the Internet through you Mac. The network interface that is used to share your Internet with Parallels is a virtual network interface, so no worries.
On a side note, if you change between an Ethernet and Airport connection you will have to go back in to System Preference's Internet Sharing click Stop, change the adapter that you are sharing from to your current method of connection and then click start again. This may require you to reboot Windows from within Parallels.
Hope this helps,
Ryan