How does each new cell get a complete set of chromosomes?

This depends on what kind of cell division we are talking about. If this is singular cellular splits, or mitosis, then there are fewer steps than meiosis, or sexual reproduction. In mitosis, the chromosomes are doubled, pulled to opposite sides of the cell, and the cell splits, resulting in each cell having a full set. In meiosis, cells split two times, meaning that each resulting cell has 1/2 of the normal amount of chromosomes. So, two of these cells (one from one parent and one from another) combine to form one cell with a complete set.