Well:
Good Luck with that. Although not essential for success, I'd suggest:

Contemparaneous Notes - The most important of all: You, or a rep, should take thorough notes as you go along. Making a written record of everything you and they say can intimidate bosses making weak cases, and make it easier to win an external solution if needed.

Representation - Ideally you'd be in a union, but even a trusted colleague can help. In any case, you probably should be allowed time to privately talk tactics beforehand. A rep can provide you with a witness if needed, and helps cancel out the employers classic tactic of a "2 managers versus 1 of you" advantage. There is a risk of management retaliation against your rep to consider.

Evidence - Accusations from them (or you) should be backed up with proof, not opinion. You might want to see or request a copy of their evidence, since they instigated dismissal they should be able to offer proof to support themselves.

You can't stop them introducing surprise evidence, stuff you didn't know existed; but you might be able to object if they do, and in the long run that trick could even help you.

Civility - Politeness from you helps you, both now and later. It's hard to fight, but rudeness can just confirm their belief in their position: "Confirmation Bias".

Focus - Don't be flattered or distracted by empty compliments; Work out your approach beforehand; work methodically towards your goal; ask questions again if they aren't answered the first time; don't be rushed into an early finish.

Breaks - If the appeal goes on, don't be afraid to suggest a short break; for toilets, food, air, water, conferring with your rep, or letting the panel find answers to your questions. If they refuse it might make them look bad; and if you're lucky they'll appreciate a little rest as well.

( Disclaimer: I am not a relevant professional; and while I've "won a few battles" with my last terrible employer, I ended up "losing the war" with a delayed, fabricated, and unfightable dismissal, my health in ruins. It's possible that leaving works out better for you. I'd have given you better advice with more time and more detail; but I hope this helps. )

Anyone got anything else?
(The Incredible Sulk Finally remembered his password on, Thu 26 Aug 2010, 1:03, Reply)