I hope you weren't expecting a comforting answer.....
The Incorporated Society of Musicians in the UK publishes rates for this kind of thing. For an orchestral piece the typical rate is between £500 and £1000 per minute of the piece. In other words, for a 20-minute concerto you're looking at the price of quite a nice car.
Do you still want to contact the composer? OK, if that price doesn't put you off, go via the composer's agent if there is one. If you want it on the cheap, go to the composer, preferably via a mutual friend who can introduce you and smooth the way to a deal!
Topic: Commissioning a work