During the cell replication cycle there are two major "phases" that the cell goes through. The beginning and majority of the time is known as Interphase. Interphase is 80% of the total cycle and is where the cell does most of the work in replicating organelles, chromosomes, and preparing to undergo Mitosis which is the actual splitting process where one cell becomes two.
During Interphase there are 3 major steps, G1, S, and the G2 phase. In the G1 phase the cell begins creating all of the proteins required to build chromosomes and DNA. During the S phase the cell replicates the chromosomes by taking one chromatid and effectively doubling it (these are later ripped apart during Anaphase in Mitosis).
So during the S phase of the Interphase cycle, chromosomes are replicated into two sister chromatids. Normally after this phase there is a check off to make sure nothing went wrong with the replication however should there be any mutations that will create some new DNA form this is where it would be made.