Denied unemployment, how do I appeal? (update)

My claim was denied after 3 weeks of waiting, and the letter says I have a short window to appeal. I worked as a teaching assistant before this. 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.