If you're fired from your job, you should be able to get unemployment compensation. The purpose of the benefits is to tide over employees who are out of work through no fault of their own.
That last phrase is the key to most of the controversies over unemployment benefits. Assuming you have enough calendar quarters of work under your belt, you can get unemployment, even if you worked part time, if you are not to blame for your unemployment.
These are the things the claims examiner (the person on the phone) and the hearing examiner (the lawyer who hears the appeal) listens for.
You quit the job. You can get benefits if you quit for a very good reason. For example, you were being sexually harassed and the employer did nothing to protect you. Or you were told that your job would be relocated to Nevada, and you can't leave your family. These can qualify as good cause to quit. You have the burden of proof.
If you were told that you could either resign or be fired, this is not the same as quitting. You are not voluntarily unemployed.
You were fired for a reason you had been warned about before. Many people are deprived of their benefits for a number of weeks, or until they get another job, on the basis of misconduct or gross misconduct. When an employer wants to object to unemployment benefits, this is the reason they usually use.
Lots of things can amount to misconduct, and some are so obvious that nearly everyone would agree. Stealing from the company, smacking the boss, threatening to blow the place up, not calling in for a week – these are all misconduct. The more subtle ones are often tied to notice of the rule: did you violate a policy that the company has published, or keep doing the things that you had been warned not to do? Examples are employees who continually come in late after being warned, employees who violate policies about counting the cash or securing the premises, health care employees who ignore needy patients.
It's not misconduct, however, if you were fired because you could not keep up with the work, or you are deemed incompetent. In that case you are not fired for a reason you could control.