You can only insert a column break (and have it visibly work) if you have
first set the text to be in two columns. Easiest way to do that is to type
the text, then select it all, then use the columns icon (click and hold for
a dropdown) on the formatting toolbar to set the number of columns you want,
and Word will put in the needed Continuous Section Breaks before and after.
Then insert column breaks as desired. (You can also set the columns on a
small selection of text, then keep typing within them).
However, if you want the columns to be independent of each other, creating a
table with two columns might also work, depending on how long the doc is.
Under Table | Properties, you can set the Border to None to not show the
lines when printing.
If that doesn't help entirely, post back with OS and Word version numbers,
and what View you are using. Columns will not show up in Normal view.
DM