There are several ways this can be done. The best solution depends on each merchant's needs and whether or not phone/fax sales will comprise ALL of their sales or just PART.
One way to do it is to key enter the info through a virtual terminal.
This is really the best way and the most convenient as well as the most flexible.
It is also possible to have a properly configured terminal machine setup for MOTO processing and key it in that way but... this is not usually recommended due to the unnecessary cost of the equipment for a MOTO merchant.
A third way is to use a PhonePay or Dial-Pay option. This option is sometimes not listed or downplayed by processors since it doesn't let them get an equipment or gateway sale
but it is available on almost every processing network.
It is not as convenient - in fact it can be a PITA to use sometimes and takes longer to process. It is only recommended for merchants that run through a few trans per month. For instance, you might have a MOTO (mail-order/phone order) merchant that does big sales but only a few per month.
Those are good candidates for a phone pay service but I'd suggest a gateway implementation w/ virtual terminal for the majority of these merchants as they will be a LOT happier with it.