The typical charge that would apply in a case with these details is called "Breaking and Entering". It basically means the accused trespassed on someone's property, forcibly entered the premises, without the owner's permission or knowledge. It's a serious charge.
The fact that the person is 16, and that no one was home or hurt, and no weapon was used are what is known as "mitigating factors", that might lessen how aggressively the prosecutor would pursue the case. In all likelihood the person would be charged as a juvenile, and sentenced to community service or some time in juvenile hall. The absolute worst case scenario would be that the person would be sent to juvenile hall until they are 21 and no longer able to be held. That is unlikely and extreme, however.
The best chance for this person is to cooperate with authorities, tell the truth, offer restitution for any damages, and a written apology to the owner and the Judge. It's called a plea for leniency. Also, and this is very important, be sure that person talks to a lawyer (I am not one) and gets advice about the laws in the state where the crime took place.
This person will probably be charged with " breaking and entering" which is a felony in all jurisdictions. You relay some good information in the question. You mention that no one was hurt, nothing was stolen, and a weapon was not used. This is all very good news because anything to the contrary would compound the situation and make the charges more severe. That being said, B and E is still a very serious criminal charge.
The DA or District Attorney in your jurisdiction will decide whether to prosecute the crime or not. Given the offenders background (never been in trouble before) and the facts of the case, the lack of aggravating circumstances ( no weapon, no theft, etc.), and the age of the perpetrator (young), the DA may choose not to prosecute this crime at all. However, if prosecution proceeds, the offender will probably get a probated sentence, or be placed on probation. I seriously doubt any jail time will be served in this scenario. Further, I doubt that any detention whatsoever will occur.
One the other hand, if it is an election year (DA's are elected), you could very well be made an example and you could be prosecuted fully. You could be sentenced to a year in jail, but then you would probably get out after serving a couple of months.
I strongly suggest you contact a reputable criminal defense attorney if you haven't already.