1) A three phase motor will run on single phase, but will not self start. Some people who use this method put a knob or sheave on the shaft and roll it with their foot or wrap a cord and pull on it much like you would start a small IC engine. For obvious reasons, many people do not like to kick start a large motor.
2) Self starting is done with capacitors. If you Google on it you will find many plans. Here is one:
https://www.metalwebnews.com/howto/ph-conv/ph-conv.html
3) Static converters are sold for running 3-phase motors off single phase.
4) Newer VFD (variable frequency drives) generate 3 phase from single phase electronically and provide speed control. They work great. My drill press and shaper are both run by them. The range of speed is nice as is the power delivered. In fact, I converted the drill press from single phase to 3-phase just so I could use a VFD.
With #1 and #2 it is common to have at least two, three-phase motors. The first motor is an idler and generates the 3-phase current for the other working motor(s). It is not used for powering any tool, usually. The idler motor should be larger than the working motor. If you have many motors in parallel , the largest working motor should not be larger then the sum of the others.
In my shop, I use a 5 HP idler motor to run a 1.5 HP lather and 2 HP mill. The idler is set up as a self start. I have been using that system since 1985. The mill and lathe run fine, even at the same time. I was advised at to outset to use a "heavy iron," older 3-phase motor as the idler -- the type that took of lots of space and needed a crane to move. I couldn't find one, so I just used a modern 3-phase Baldor.
With method #3 the motor can be used for power, but the static converter is expensive. See: **broken link removed** Cedarberg has been around a long time and works well.
Today, I would and do use a VFD running from single phase to run a 3-phase motor in a shop without 3 phase.
John