We use the word "common" all the time. It's basic vocabulary. It means something that happens frequently, or something normal, or something almost everybody does. "Where I live, snow is common in the winter. Therefore, it is common to own a snowblower."
"Commonplace" is used much less often. As a learner, it is not a word you will need to use yourself. We would be more likely to say "everyday" or "ordinary." According to one online source, "common" is among the 1,000 most frequently used words, and occurred at least ten times as often as "commonplace."
In US English it is slightly literary or old-fashioned.
"Commonplace" always carries a sense of being boring. It is something automatic, or uninteresting. It does not draw your attention. You do not think about it much.