Filing for unemployment is easy. In some cases, you can receive benefits even after getting fired for some foul shit you've done, provided that you lie about the circumstances surrounding your termination, but that depends on if your employer wants to go through the hassle of attending a hearing by the employment commission. If they don't/can't, the State will award you the benefits by virtue of your former employer's absence from said hearing or if your former employer is unavailable to otherwise contest your false recollections of the exact reason(s) for your release.
Traditionally, however, the mandatory requirements for unemployment eligibility is dismissal from work through no deliberate fault of your own (e.g., budget cuts, employer found someone more experienced to replace you, etc.) and - this is more important - the length of your employment. In some States, you don't necessarily have to be with that one company for a while, but they definitely want to see a recent history of steady employment within a certain time window (like 18 months).