If your modem is connected to the computer via USB, it may be that Linpus on the One is intended to connect to the Internet only via Ethernet or Wifi. They have cut down the kernel so that it contains only the bare minimum of software. it is this lack of flexibility that allows it to be so straight-forward to use and fast to boot.
Two options :-
You can install Ubuntu onto the One via a USB CD drive and people have had some success getting the newer/odder bits of the Acer's hardware (think wifi, microphone and camera) to work, or you can find out what software needs to be added to Linus to support your USB modem and install & configure that.
If you connect via Ethernet, then Raido is most-likely right.
If you have multiple machines wanting to access the Internet, you would usually be far better off setting up a local network with a router 'sharing' your Internet connection.