How do two sets of chromosomes split up during meiosis without staying the same?

We have two sets of 23 chromosomes, one set from our father and one set from our mother correct? What I'm trying to ask is when it comes time for our body to make cells, how do these 46 chromosomes split in a way that each daughter cell gets chromosomes 1 through 23 instead of say, one of the cells getting two 7th chromosomes and the other getting two 14th chromosomes? Also, is DNA ped down in whole chromosomes? Or do the chromosomes recombine themselves somehow?