Don't mind Bob and Forrest, they're just having a bit of fun. They will be two of the best resources on this site as you get more into this.
Anyway, a VFD is an electronic device that allows you to control the speed of a 3-phase AC motor. Another benefit is that they can convert single-phase input to 3-phase output. This makes them ideal for home shops, especially if you are only going to run one machine.
VFDs are great devices, but they do have limitations. The main one for machine shop use is that they cannot be used as 3-phase "power supplies" like RPCs. In other words, you cannot plug in a bunch of stuff to the output of a VFD and switch loads on and off while the VFD is running. They are designed to operate 3-phase motors only, and if you want to switch the output of the VFD from one motor to another, you need to stop the VFD, make the switch, and then start the VFD again.
In your case, you will need a VFD that is capable of single-phase input (assuming you only have single-phase at home) and is rated at least 1 Hp. Some VFDs are fully rated for single-phase input. In this case, just get a 1 Hp and you should be fine. However, some others are only fully rated for 3-phase input and require derating when used with single-phase input. In this case, you will probably need a 2 Hp unit to run your 1 Hp motor.
Now for the sales pitch: I happen to work for a VFD manufacturer called AC Tech (
www.actechdrives.com). We make a few VFDs that would be perfect for your application. We even make ones that will run from 120 Vac input and give you 3-phase 230 Vac output. If you are interested, let me know where you are located and I'll put you in touch with a local AC Tech distributor.
I'm sure other contributors to this site will have other suggestions as well.
Good luck!
John