My experience,for what its worth, is that politness counts for everything, But first and foremost..ALWAYS wear a shirt and tie, clean shoes (not runners/sneakers) and trouser (not shorts)
Ask for the duty manager, check in staff rarely have the authority to upgrade,
If you have a frequent flyer card, show the duty manager it. If you do not have one, apply for one now, remember they are free and the duty manager , on seeing you card has no idea how many points / miles you have accumulted unless its a gold / silver status card
If its possible to be upgraded, you will probably not hear about it untill just before boarding, as business class passengers can turn up at the last moment, so have patience and wait around an area where the duty manager can see you.
If it does not happen, be polite to the duty manager...you may travel again and see him some other time. Upgrades will best happen at times when flights are overbooked, friday evenings/Sunday evenings, Summer, holidays (Christmas )
Remember dress well and be polite
Good Luck
It's worked for me on many occasions..!!