Trizol can extract RNA/DNA/Protein. You can use spin columns to further purify RNA/DNA. For protocol details google Trizol protocol, it is readily available.
It depends for which applications you need the DNA.
For sensitive analytical techniques (especially sequencing) is the DNA quality not adequate. And you have the risk of contaminations between your samples
(and health and safety problems with organic solvents, too).
I would prefer a column (silica-membrane).
It allows increased throughput in a shorter time.
And you recieve a increased yield of recovered DNA with a better quality of purified DNA.
It is a little bit more expensive but you will have more fun with your DNA later
I would not suggest Phenol-Chloroform Extraction anymore!
If you have a good touch/feel for the function of a silicamembrane you can build an own one (silica beads are not so expensive).