Prophase- In the first half:The chromosomes start to shrink. The cytoskeleton begins to form the mitotic spindle, which will grow between the centrosomes and organize the chromosomes.The nucleolus goes away.
In the second half: The chromosomes become extremely compact. The nuclear envelope disappears and all the DNA comes out. Some of the mitotic spindle starts to catch chromosomes.
Metaphase- The mitotic spindle moves all of the chromosomes across the middle of the cell.
Anaphase- The two chromatids of each chromosome are pulled apart from each other and become their own chromosomes. Loose microtubules push the ends of the cell to make it longer.
Telophase- The mitotic spindle is broken back down into microtubules. Two new nuclei appear (one for each new cell). The chromosomes return to their normal form (not all squished down).
Another big step is cytokinesis, which starts either during Anaphase, or Telophase. In animal cells, the cell is pinched around the middle to create the two new cells. In plant cells, a cell plate comes into the middle of the cell and separates it into the two new cells.
The main four steps can be remembered using the acronym PMAT.