Got a denial letter for unemployment, what now?

My claim was denied after 4 weeks of waiting, and the letter says I have a short window to appeal. My employer's version of events does not match mine, and I have emails that show it. If you have appealed before, what helped you prepare?

Stay calm and stick to facts. Mine lasted about thirty minutes and felt more like a conversation than a trial.

I printed my emails in order and wrote a one-page timeline. The hearing officer kept going back to it.