It's actually, pretty simple. Enforce the existing laws, crack down hard nationally in all 50 states, and then deport as many illegals as the Border Patrol/ICE can catch. If the illegals have dependents who are American citizens, then they can go back with their parents and return when they are 18. I don't care if they are children or not. They are still illegal.
As Eisenhower's men found in 1954, once the crack down starts, the illegals will mostly deport themselves. Just look at what happened in Arizona and Alabama when they toughened their laws---entire illegal alien communities simply packed up and left after dark.
This is not rocket science.