DNA cloning allows for the reproduction of DNA fragments. It involves inserting a fragment of interest into a vector, such as a plasmid, and introducing them into a host cell. The vector carries the DNA fragment into the host cell and allows for its amplification. The key steps are cutting the DNA fragment and vector with restriction enzymes, ligating them together, transforming the ligation product into host cells, and selecting for recombinant clones. Colonies containing the insert DNA can be identified through blue/white screening which detects functional LacZ genes.