If you have worked the first 4 of the last 5 work quarters (that is you were employed during the first 12 of the last 15 months) and you are fired for a reason other than your own misconduct, then you will qualify for benefits. Misconduct is willful and wanton disregard of the employer's interest, or of the employer's reasonable standards of behavior or, otherwise, the actions of the worker must show gross negligence (for example, giving wrong medication to a patient).
However, the mere inability to do the job, or good-faith errors in judgment, is not considered misconduct in an unemployment compensation case. The employer may not like you or treats you badly because he is simply a miserable person, but this is not misconduct for purposes of the unemployment compensation law.
To prove misconduct (and disqualify you from benefits), the employer would have to show the unemployment agency, through testimony and, if possible, documents, that there was an employer policy on the particular conduct involved, that the policy was applied equally to all employees, that the employer had not previously condoned the actions that resulted in the discharge. Usually they have to show th claimant had received warnings about infractions, and that the claimant continued in the misconduct after the warnings. However, in the most serious offenses, warnings need not be given prior to discharge, in order for the worker to be disqualified for unemployment benefits
One word of caution though - quitting because of a personality conflict will result in your denial of unemployment benefits; so don't quit.