Denied unemployment, how do I appeal?

My claim was denied after 20 weeks of waiting, and the letter says I have a short window to appeal. There are 16 people counting on me, so I am trying to be careful. 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?

Thanks for writing this out. I went through something close to it 14 months ago, and it settled down once I kept a simple log of every call and form.