Fantasia Sam is right - you have more chance of being upgraded if you fly scheduled, not charter. You need to look reasonably smart (but I don't mean suits!). Also, if you have young kids, then you have next to no chance. Business people don't pay £3k for a business class flight to have kids crying next to them (sorry - but that's what they think!). It may help to be one of their 'frequent flyers' too.
Scheduled airlines regularly overbook flights as there will always be people who have to change their plans or don't turn up. Charter flights are used by people going on their holidays and don't get overbooked as (generally) everyone turns up. If everyone turns up on a scheduled flight which is overbooked, they 'bump' passengers. Initialy, they look for volunteers and may offer free upgrades if you are prepared to delay your travel by a day. This happened to us last year, and we were given free hotel accommodation and compensation too. If they don't get volunteers, they will involuntarily bump people.
You may get a free upgrade, if you are very very lucky - but it's always best to assume you won't- then you won't be disappointed!
I was amazed when we got a free upgrade to first on the internal part of our return flight (MCO to Philadelphia) - and we hadn't even asked for it. I still don't know why they gave it to us!
We have been able to book an upgrade on our return journey by collecting frequent flyer miles and 'buying' some extra miles. It has cost us about £70 each. Trouble is, it spoils you - it's hard sitting in 'coach' when you've tasted the champagne & smoked salmon in business class!
Julie