Assuming you have just been denied unemployment benefits by the initial claim determination, (vs. being denied after a first level unemployment hearing decision), it's a simple matter to write an unemployment appeal letter.
After all, you do have a valid reason for disagreeing with the unemployment denial because it was erroneous (unemployment jargon for incorrect) .. don't you?
If you're in the dark about what your employer's story was, or don't know if they might of submitted documents to the state to weight their story, request your state claim file .. so you know more about why you were denied.
After you send a very simple and non-disqualifying appeal letter .. in a timely fashion to beat the deadline for appeal (found on all initial claim determinations) all you have to do is NOT sit back and relax, but learn what you need to do to prepare to win the first unemployment hearing .. they way the unemployment appeal section expect everyone to do.
By the time you receive the notice of hearing from the state time, and listed issues you'll finally have your last opportunity to argue why the state was wrong to side with the employer the first time out.
This appeal is your last chance. Anyone who tells you there's a second chance appeal if you don't win the first hearing may not of explained why I know it to be unwise to use a second chance appeal as a fallback position should you lose the first hearing.
I explain the danger as I see it, of appealing to an unemployment insurance board of review here.
Learn how to take control of the situation and learn about the burden of proof.
Who knows, you may spot an advantage when you learn what needs to be proven .. or possibly disproved to finally collect, even if you were denied unemployment benefits erroneously .. after you first claimed you lost your job through no fault of your own.