Got a denial letter for unemployment, what now? - what worked for you?

My claim was denied after 4 weeks of waiting, and the letter says I have a short window to appeal. I worked as an HR coordinator 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?

Thanks for writing this out. I went through something close to it 11 months ago, and it got easier once I kept a simple log of every call and form.