Denied unemployment, how do I appeal? - any advice?

My claim was denied after 3 weeks of waiting, and the letter says I have a short window to appeal. It has been a long 3 weeks. 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 10 months ago, and it settled down once I kept a simple log of every call and form.