Chromosomes organization

In any human cell, there is (or should be) 23 pairs of chromosomes - 22 pairs of autosomes (i.e. non-sex chromosomes) and 1 pair of sex chromosomes - in males that's an X and a Y, in females that's two Xs. While the autosomes are homologous to each other (as well as the two X chromosomes in females), I wouldn't say that the X and Y chromosomes are homologous as the Y chromosome is missing many of the genes that are found on the X chromosome. This explains why many X-linked conditions tend to only affect males.

During prophase (the first stage in mitosis or meiosis), the DNA replicates and the DNA then condenses into a tight structure known as a chromosome. Since the DNA that makes up the chromosome has already undergone DNA replication, there are two chromatids. The two chromatids that make up the chromosome are identical to each other, and are joined at the centromere. So at this stage, there are 46 chromosomes (remember, 23 pairs) and 92 chromatids (since at this stage, each chromosome is made up of two identical sister chromatids). Then, during telophase the chromosomes are aligned at the equator of the cell by the spindle apparatus. During anaphase, the spindle apparatus pulls the sister chromatids to opposite poles of the cell, causing the chromosome to break apart at the centromere. Then the cell splits in two and the two daughter cells are genetically identical.