Working with children in any sense is not easy. When you need to run a professional work environment it is next to impossible to get kids to do things in a way that completely matches an adult set. This being said, there are certain ways to deal with young people so that you can get the most out of the situation.
One of the most common problems that people encounter is that kids have a short attention span. Often times scenes require a great amount of time waiting for the actor, especially in between takes. Work out a few ways to entertain the child in these down moments and get everyone in the cast and crew in on it. See if you can't make it somehow related to the scene so they stay somewhat in character.
The work itself is also going to be difficult for the child to stay focused on. Try to shoot scenes in smaller increments than you normally would so the kid is able to keep their head in it. It will be even better if it is just a few lines at a time and ran through as quick as possible. Try to set up a system of rewards with them to give them goals.
You will find that many younger children do not understand what acting really is and think that it is just memorizing lines and saying them at the appropriate time or knowing when to move somewhere at the right time. This may lead them to look around the set, not get into character at all, and behave in an unnatural way for the scene. Try to explain this too them as best you can and direct their every body movement in the scene.
End of Scene Focus
If they are very young children they will have a tough time staying in the scene once they have finished their lines because it is natural to look for the nearest authority figure or parent. Make sure that they know they have to stay looking in a certain direction, and if they cannot do this try putting their parent in the general region they are supposed to be directed toward.
Make sure that the children themselves come from at least somewhat of a professional environment, whether this is an acting background or otherwise. This usually just means that they have some structured commitments in their life where there are expectations on them. This does not have to be work, and it can even be things like team sports or dance lessons. The parents also must have a good synergy that matches supportiveness with an understanding of what this unique situation requires.
You are going to be subject to a number of legal and union restrictions when working with children, so these must be looked into before filming. This can get your entire production into a lot of trouble if they are not observed, so try to arrange the shooting schedule around this.