When I researched this, and talked to some electrical engineers about it, I found out it could be easy or hard. There are three ways to convert single phase power to 3 phase.
1. There is the static phase converter, which is usually the cheapest, but has the downside of eventually burning up whatever motor it's powering and never allowing the motor to deliver full power. The reason is above my level of electrical understanding, but I think it has something to do with it not actually creating three phase power. I never went any deeper into researching them after talking to people that had used them.
2. There is the VFD, or variable frequency drive. These are sort of like the converter above, but they don't burn up motors and they do deliver full power. There is also the added advantage of fine tuning your motor speed with one. For smaller motors, they're not that expensive. I paid right around $140 with tax several years ago for the one that's on my South Bend lathe. That said, it's for a 1 hp motor. Aside from the crappy instructions that came with it, mine was easy to hook up, and the speed control is pretty nice since the lathe only has six built in speeds.
3. There is the RPC, or rotary phase converter. These are basically just a three phase motor with some extra stuff added on to make them easier to use. They're pretty expensive to buy, but you can build one yourself(lots of info on the interwebz). It's been a while, but if I recall correctly, it's better to have one that is slightly larger than the motor you're trying to run, but not a whole lot bigger. For example, it wouldn't be good to have a 10hp RPC if you only needed to run a single 1 hp motor. All that I really understood on this was that the RPC needs a certain "load" to create 3 phase power at the right voltage and "balance" that voltage across the individual legs of said 3 phase power. The simplest way to build yourself a RPC is to get a three phase motor and wire it to the motor you want to power. Run single phase to the "RPC" and make sure you have a switch to turn it on and off. When you want to start the RPC, turn the power on and use an old style lawnmower pull rope(If you remember the kind you had to wind yourself) to start the RPC. It will take the RPC a minute or so, but it will come up to full speed and then you can start the equipment you want to power. A three phase motor will run on single phase power, and produce three phase power, but it will not start on single phase, which is the reason for manually starting it. The commercial RPC's, and the good versions of plans for home built versions, will include some start capacitors and a few other bits to eliminate that manual pull rope starting thing. The really advanced ones have an auto sense and will automatically turn on when the equipment they are supposed to power is turned on.
Your last option is to repower it with a single phase motor, but that may be just as expensive as an appropriately sized VFD or RPC. The other downside to going to a single phase motor is that they have less starting torque than a 3 phase. I don't think it would matter in this application though. If I had to do it over again, I would probably go ask my wife's stepdad to help me build the RPC since I already had a brand new 5hp three phase motor to do it. Something I forgot to mention earlier is that the RPC has another advantage in that it can power more than one motor at a time, whereas the VFD cannot.
