Also, would you say something different whether that person is someone you know or not?
There is no most commonly used way, it depends on the situation.
- わりい (←sounds like you aren't really showing remorse, male)
- 悪い (male-ish)
- すまん (male-ish)
(If you say any of these twice in a row, like ごめんごめん, that also makes it sounds like you aren't showing remorse.)
- 申し訳ない (feels proper but not particularly polite due to ending with a plain ない)
- ごめんなさい (feels slightly childish)
- すいません（でした） (probably the most common in everyday non-business speech)
Often prefaced by 「大変ご迷惑をおかけして」 or similar, depending on how bad of a thing it was.
Especially in business, there are plenty more variations, but I'd say these are the more commons ones.