How do you get into the high level private pilot industry? (like flying CEO of companies)

The pathway would be very similar to becoming a pilot for an airline. You would probably earn a number of licenses in roughly the following order: Private Pilot License > Instrument Rating > Commercial Pilot License > Certified Flight Instructor. Along the way, you would probably learn how to fly some different types of airplanes such as those with more than one engine (i.e. get a multi-engine rating) and/or possibly jet engines.

For the high level jobs, you would probably be required to have an Airline Transport Pilot (ATP) license. The requirements for this can be found online at: http://www.ecfr.gov/cgi-bin/text-idx?c=ecfr&rgn=div5&view=text&node=14:2.0.1.1.2&idno=14#14:2.0.1.1.2.7 In airplanes, you would need to have at least 1,500 hours of flight experience to obtain an ATP license. For most of the private jet operators like NetJets, FlexJets, etc. they will want you to be more experienced, and the airlines are a common place to build this experience.

There are certainly other paths, however, it usually comes down to having the right licenses (i.e. ATP), a minimum number of hours (probably 3000-5000+ hours) depending on whether you would be a Captain or First Officer, and the right kind of time (i.e. multi-engine, in a particular type of aircraft, etc.). You can search the pilot qualifications that companies require, one example is NetJets: http://www.netjets.com/Careers/Pilots/ The way to build time and experience without paying for it typically involves some time being a flight instructor and also going to the airlines. An alternative way to build experience is also joining the military. The military operates a lot of advanced and sophisticated equipment that will probably help meet a lot of multi-engine/jet/instrument experience requirements.

Josh, being a pilot is cool, but it will get boring in time. Basically flying a plane is a lot like driving a bus with wings. In fact one of the major aircraft builders is called AIRBUS. Think beyond being a pilot to being the guy who owns his own charter airline. Imagine always having the freedom to fly anywhere you want, anytime, as a business expense. Think past step one because step three or four is always way more awesome!