This crime would be a misdemeanor in Nevada because the goods that were wrongfully taken were under $650. The maximum amount of time a person could do on a misdemeanor charge is 6 months in jail but there is no minimum. That is, any amount of time up to 6 months would be authorized under the statute but no incarceration would be necessary at all.
I don't know why your fiance was physically arrested on a first offense, but if he pleads not guilty -- which is the plea that he should make in order to keep his rights open so that he can negotiate a favorable deal -- on a first arrest of this sort he would typically be looking at nothing worse than probation with restitution to the pizza place.
I would expect him to be released on his own recognizance at his arraignment when he comes before the judge, as it's his first offense and a non-violent crime. If not, you would want to bail him out because he will get a better deal from the DA if he's out rather than already in jail.
Ideally, you'd want this off of his record if he could get it deferred. A deferral is a special form of probation where after he pays his fines, does some community service, takes anti-theft classes and stays out of trouble during his supervisory period, the charge against him can be dismissed. Then he wouldn't have to carry around a criminal conviction. That's important because a theft conviction, even for a misdemeanor, can have a major impact on his ability to find a good job and to advance professionally. Employers tend to shy away from hiring thieves.