As Kief stated VFD's do change AC in to DC but the DC is Made into a DC square wave Similiar to an AC Sine wave. The Motor sees it as an AC signal though. For a little more information The only Way to change the speed of an AC motor is to change the Hertz (HZ) In the USA our power comes to us at 60 HZ in other Countries it is 50 HZ. Hertz is how frequently the AC is switched from positive to negative thus creating the Sine Wave. Thus the VFD was developed to change the hz of electricity to change the speed of an AC motor. Until recently that is what these were used for, but for a small amount of money manufacturers were able to offer a unit that would accept an single phase input to 3 phase output. I hope this gives some what of an explatation of how they work.
Also not all VFD's will accept a single phase input so if looking for one get the correct model.
Also not all VFD's will accept a single phase input so if looking for one get the correct model.