Does using CRISPR/Cas9 knockout need to add donor DNA in the process?
Short Answer: 
No, for CRISPR/Cas9 knockout you do not need to add donor DNA.

Little bit more detail:
CRISPR/Cas9 allows you to cut at a given position (defined by the gRNA). This will lead to double strand breaks (DSB).

If you do not add any donor DNA, the cell's DNA repair mechanism will try to repair the double strand break. Since these CRISPR/Cas9 mediated DSBs usually have a blunt end it is really hard for the DNA repair mechanism to fix it. If will often introduce an error, for example by missing a basepair (or several) leading to a frame-shift mutation. This DNA repair mechanism is called Non-Homologous End Joining. 

If you do add donor DNA it will contain both the sequence you want to introduce (say a green fluorescent protein) and homologous sequences on both sides of the double strand break. In other words, if you want to cut the sequence ATCGCA exactly in the middle you will get ATC and GCA. You want to insert AGA. The donor plasmid must then have the sequence ATCAGAGCA. As the cell now has the homologous regions, it will use the Homology Directed Repair mechanism.

The sequences are for illustration only - in reality a gene is usually several hundred basepairs and it is recommended to have much longer homology regions.