The service in the US is usually called Call Forwarding. A "glitch" in getting it is that, although that function is fairly inexpensive, you can only get Call Forwarding if you also get Caller ID, and Call Waiting, and ... so the "extra services" are really available only as part of "packages" that add noticeably to your monthly bill.
Allan C. -
If you have "call waiting" an incoming call often will break your internet connection, so it's common to set up the dial-on for your internet connection to send the code to disable call waiting before it dials the phone number for the ISP. This should give a caller a busy signal while you're on the web.
If you don't disable call waiting, the caller often will hear it "ring until answered," and of course if you're on the web you won't hear it ring, so it won't get answered.
Note that specific "extra functions" may differ depending on where you are and who provides the service.