Denied unemployment, how do I appeal?

My claim was denied after 4 weeks of waiting, and the letter says I have a short window to appeal. I worked as a payroll clerk before this. The letter lists a deadline and a hearing process, but it is hard to follow. 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 got easier once I kept a simple log of every call and form.