Denied unemployment, how do I appeal? - what worked for you?

My claim was denied after 9 weeks of waiting, and the letter says I have a short window to appeal. Any experience at all would help. My employer's version of events does not match mine, and I have emails that show it. Should I ask someone for free legal help?

Thanks for writing this out. I went through something close to it 6 months ago, and it settled down once I kept a simple log of every call and form.