I love this idea. Not as something to realistically help you get started, but purely educational. There's so much knowledge tied up exclusively among people "in the industry", that would be great to get out into the public. I would love to know all the things involved in starting an airline. How are planes actually bought? How are mechanics actually procured? What kind of safety regulations are followed? etc. I once…
1). To acquire aircraft you either buy directly from the manufacturer (Boeing, Airbus, Embraer etc.) or (much more commonly and especially if you only plan on operating a small fleet) you lease them from someone like Macquarie or, in some cases, from another airline who has spare capacity (known as wet and dry leasing).
Alternatively, if you are an existing airline, you can temporarily contract another airline's aircraft under what is known as ACMI. They give you their aircraft and crew and you pay the fuel, landing fees and other taxes. ACMI contracts can be as short as a day or last for years.
2). For mechanics (assuming you mean people), you either hire them directly via specialised aviation staff agencies or you outsource maintenance (e.g. to someone like www.priority.aero)
3). Safety regulations are devised by international bodies such as ICAO and IATA as well as national entities known as Civil Aviation Authorities. Aircraft manufacturers also play a role. It's typically each country's CAA that primarily enforces the regulations on all nationally registered aircraft. In Europe, there is also Eurocontrol which is a pan European governmental body that's responsible for co-ordinating Europe's airspace.
If you wanted to start a new airline (assuming it was to offer charter flights and not scheduled routes), some of the things you'd need to do would be:
1). Decide what type and how many aircraft you need
2). Decide what cabin layout you need (all economoy?, how many rows, how many galleys etc.). This depends largely on who you envisage your customers will be (e.g. are you planning to sell charter capacity to tour operators or do you want to offer a VIP configured fleet to fly wealthy people around).
3). Decide what engines you need (different generations have different range capabilities and maintenance costs)
4). Get your aircraft. If you go the leasing company route, try to get a "power by the hour deal" where you only pay for the hours you fly (the holy grail) or a short 1 or 3 year lease. The market is depressed at the moment so gone are the days where leasing companies demand 5 or 10 year terms.
5). Get insurance. You will need a specialist aviation policy from someone like Lloyds. Although it depends on what aircraft you are insuring and where you plan to fly, a typical policy will offer damage and liability cover in the region of $200 million.
6). Get your crew together (flight, operations and ground staff). Due to minimum rest regulations, you are going to need at least two sets of flight crew for each aircraft if you want to maximise utilisation. For a 180 seater, a typical crew complement consists of: a captain, a first officer, a mechanic and 4 cabin staff. To save on staff costs (at least in theory) you can outsource operations (these are the people that co-ordinate everything -e.g. catering the aircraft, filing flight plans, crew rostering, over flight permits etc.)
7). Get your operating license from the CAA. You can't fly without it.
8). Set up a fuel deal using a fuel broker (or directly with Shell or BP).
???
profit*
-- * Actually there is no profit in running an airline. Seriously, don't do it (trust me).