well, it somwhat depends on how your router works,
But for most off the shelf routers, they use something called "NAT" network address translation. There is no need to configure a proxy server.
The router will have a private IP Address that it will assign to your machine with DHCP which will include the proper routing and DNS settings (same way for Windoze as Ubuntu, and you're all set)
I have been using Ubuntu behind a router for years, no need to configure any proxy stuff.
If you want a proxy server, you can configure it that way too, but not really necessary.
Hope this helps.