What is the best way to lead a new soldier who is uncertain if they even want to be in the army?

I have seen this a few times, and most recently with a friend of my son who was expecting busers remorse.
My first reaction is always to ask why. It is very possible that there is the perception of a failure on the part of their respective branch that can be quickly and easily resolved and correct the situation.
If this is not the case, I echo what my company commander told me in boot camp. That is, if they get an entry-level separation it will affect the rest of their life. Not only will they lose any benefits they may have earned, they will not be employable by any company that deals with the government, and they will be barred from ever re entering the military. The easiest way through is to fulfill the contract.
Of course, some just want out and can't be reasoned with, and that's a shame, but you can save all of them.

be sure that if he does not want to be in, he will not get the money either.

Please note this is written from the perspective of "new" being brand new fresh off the bus new.

As a retired SFC with a lot of trail time, I had to deal with this question over and over again. By day two or three you get the knock on your office door. Q: "DS? can I speak with you?" A: "Where's your battle buddy?" (IET soldier runs off to get "battle buddy" and returns} Knock again Q: "DS?" A: "Yes?", "I think I made a mistake joining the Army". And now is when a Drill Sergeant earns his/her pay. No yelling or screaming but a guided counseling session to find out what is really bothering this young person. They all have reasons for joining. 9 times out 10 the session ends with the SM agreeing to give it a few more days and we never talk again. That leaves those with real problems that we (new soldier and their DS} have to solve together, you demonstrate that we are a team from day one and for many, it's something new in their lives. The idea that the Army is your family, there to help you .

Ok. Having spent my first two years in Baumholder Germany with a Sgt that didn't like me I felt like I wanted chartered out. I wasn't a quitter I just never felt I was needed so why stay. I succeeded by knowing I committed and no one person was able to make me a quitter. My second half of enlistment was spent at Ft Hood where value was rebuilt by positive reinforcement and rank. I felt like I was a key member of my team. When I went to ets I had a ssg treat me like crap but my immediate leader told me I would succeed and to move on cause a life as a soldier was not my calling. In business today where there is large amounts of turn over I have always succeeded in keeping employees not by promises or carrots but by instilling their individual values and helping them fertilize their own experience where they are at instead of the other side of the fence. Anytime you have an employee, in this case a soldier, you can usually find a cause and try to cure it. Must if the time an issue is not what it seems to be. I owe my success to the four years active duty Army I did. It put me in a path to a life of success as it does for many.

A leader should tell the soldier you have signed a commitment to the military. You made a commitment and need to fulfill it. The best and easiest way to leave is to follow orders and complete your enlistment. Anything else you lose veterans benefits and cause personal burden upon themselves and their unit.

Most soldiers find out the army is not what they thought it was after being in a short time. They commonly use the excuse "my recruiter lied". The fact is it's almost impossible to describe the military to a potential recruit. The truth is most young soldiers are too immature to see the BIG picture and that is 3 yrs goes by fast and the benefits far out weigh. Job trng, travel, VA benefits. Not to mention educational and the fact you served your country something you can be proud of and tell your grandkids. After all you don't want to live the rest of your life telling lies for which many do. So having said this, suck it up and deal with it, it's only 3 yrs of the rest of your life. Trust me you will be glad you did.

Many good answers here already so i have just one point. Sometimes a person joins the military with certain goels, but ends up in a rate that doesnt meet those goels. They are too new to the military to know what other rates might better suit them, much less how to cross rate to a better mos.
As we know, recruiters get incentives for fulfilling certain rates, so I imagine that is what causes this.

I did Army basic in1988 it was not as hard as Marine Core basic in the end a little suffering builds character I am glad I completed it.

Well I see both sides. On one hand you can fall on the old mentality of 'you don't want to be here, then I don't want you here's and help this Soldier return to civilian life. On the other, you kind of owe it to your unit and this Soldier to see what's going on and do your best to correct him, especially seeing as though this particular Soldier is relatively new to the Army. I think you have to take each case individually, but in the end they signed a contract, and unless you are over strength in your unit (which if you're in the Active Army I highly doubt) then you can still use this Soldier.

As I see it he has three options. He can be a pain in the ass, where as he may draw a General discharge, and the collage money is gone. He can desert, and the collage money is gone. Or he can do his job for the remainder of his contract, and get his collage money. There are no free lunches---make up your mind.