Understanding the motor load is critical to specify a VFD. There are three basic types of load; constant torque, variable torque, and constant horsepower and you only need to know which you have. The machine defines it; the VFD difference is the amount of overload they allow. There are also options available for overhauling/regenerative loads.
PWM VFDs are still the predominate type and are simple to apply. There are new VVVF drives but I've only seen them applied to elevators. A PWM VFD rectifies the AC to DC via diodes. It then "pulses" that voltage from a DC buss via IGBTs to the motor, varying the frequency. The motor accepts that power and runs happily. PWM VFDs maintain a constant v/f ratio for constant torque, but "v" is only apparent based on the width of the pulses. If you don't believe me check the output with a good digital meter and then with an old D'Arsonval meter.
There are many options available for VFDs but don't worry about them until you need them. Talk to your supplier and rely on his experience to guide you. Don't waste time trying to learn everything at once - learn it when you need it.
There are thousands of VFDs applied by non-engineers because they are not that complicated. All come with manuals with easy to follow wiring diagrams so it's hard to make a mistake. The most important question to ask, when considering a VFD, is "What is it doing?" Is it a fan, belt conveyor, etc.? After that, your best resource is your vendors. I would call several manufacturers and get all their advice, they are a great resource.
You could check with your utility company to see if they provide classes on VFDs vs. Soft Starts vs. Magnetic Starters. Usually, the classes they provide are free, when you are large user of power and they are not trying to sell you a specific product so you do not get the sales-pitch. They want you to have the correct type of equipment for the work you need done. They will provide a simplistic overview of how a typical VFD works (not manufacturer specific) which will be extremely helpful. You can learn as much or as little as you would like about a VFD.