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

Talk to them.... Encourage them... Speak of the benefits and the honor of serving... Find out why they joined and if that has changed.

Many of us go through that FTA/I'm getting out phase when we first join. It's a different way of life, and some people aren't used to being 'bossed around'. In their minds, it feels like disrespect. "You ain't gone talk to me all kinda ways. I'm a grown ass man!!" People like this need to be made to understand that the military life is a structured process of rank, authority, expectations, and growth. No one taught me this. I had to learn this, and it probably took me my first 5-7 years in to figure this out.

Soldiers like this most likely just need a good 'sit down' and talking to. Odds are, they'll never get this talk. Instead, they'll just get dragged through the ringer and sent back home, with virtually no chance to do any better than what they doing before they joined. This has become our society's way of dealing with people, taking the easiest way out instead of long term problem solving.

Had a PFC. That wanted out so every payay he would go withdrawal all his pay, go to the co's office and sign it over to him. In order for him to get out. He was still in when I left that unit.

Kicking people to the curb was not an option in the sixties. If I had booted everyone who didn't really want to be there I would have been the only person in my platoon. lol

Even though I've been an NCO for a hot minute, I have had a very limited opportunity to mentor junior enlisted (my current unit is only 30 people, all S/NCOs and one officer), but in that time, I have had more than one person voice their displeasure at their career or their circumstances. One of them was me. Back in 2014, I f'ed up bad. I won't go into details, but I was one yes/no decision away from losing a stripe. My Commander saw fit not to take it that far, but boy did I still feel the pain. By that point, I'd lost all hope for my career; I had some hefty paperwork in my PIF, my clearance was threatened, and I'd lost a lot of respect from my peers, not to mention trust from my chain. My supervisor, a crusty E-6 who was a green-to-bluer (Army-to-Air Force) sat me down and had a long conversation with me. I told him straight-up that I was thinking of letting my current enlistment lapse instead of re-upping, and he kicked me in the balls with pure facts. He asked if I had enough savings for my family (my wife was pregnant at the time and unemployed). No. Did I have a job or potential job lined up on the outside? No. Did I have any money for education? Yes (my GI Bill, but it wasn't enough for what I wanted or needed). He asked a few more like this before I got the picture. And he told me, "I'm not telling you what to do. In fact, if you want out, get out. But between now and when your enlistment ends, start getting everything ready."
After that, I hit the books at work (earned the top performer rating not long after), earned some more college credit, took on a subordinate, attended a class, pulled myself out of debt, built up some savings, etc. All with the original intention of being all nice and shiny for when I got out. Turns out that crafty bastard mind-f'd me; doing all that reminded me why I joined in the first place and I was actually thinking less and less about getting out. Actually just extended my enlistment a few months ago through 2017.
My point being, sometimes you gotta get creative with these people. Always offer them the fork in the road; the military doesn't need people with no desire to perform well in it, but the choice will still be theirs to either recognize that they are not fit for service anymore, or to recognize they can improve and start shaping up. And no matter what they choose, as an NCO, it's your job to set them up for success no matter what the choice is.

A very good question. You need to talk to him. Get yourself ready to have a professional and personal growth counciling. He is probably weighing his options. You need to remember that anything he decides is about himself and not necessarily a condemnation of your leadership skills. Talk to him about what he wanted to achieve through the Army. If he still decides to leave let him know that he still has a job to do until then and assist him with the transition process. I told my guys that whether or not they are still my soldier, they can always come to me with their problems. I still listen whenever my old soldiers need to talk to someone and I've been out for 3 years. Remember that your guys are like family and we don't stop caring because someone moves on.

Be the leader-> have a counseling session (non-4856) and listen to what they have to say. Sometimes the solution is right there and that soldier just does not see it.

Thats the issue I see in the Army today. Many junior leaders put on stripes and let the power go to their heads. They think from "9-5."

Always be there for them, make it easy for them to come to you when they need help. If they mess up, tell them what they did wrong and correct them. Make sure they understand there place and that they understand yours. And lat but not least always lead by example, show them that the army in reality isnt all that bad, its not perfect but its what you make of it.

If they are contemplating leaving the Army so soon into joining, they probably don't know what all the Army has to offer. Their are options to reclassify, there are schools to attend, there are identifiers for many jobs as well. I've seen to many loose motivation and hope and lean on the uncertainty of their former civilian life (when they return to it, they usually regret it). It takes a true leader to address their concerns and aid them in pursuing their goals (through the Army).

Show Him everything about the army like you were shown and see how much he retains and his he motivated in what he does.