Write someone's name in red during funeral rites or to indicate that the person is dead. This is the primary reason for the taboo in Korean culture, and why it should be avoided. It can also be used when writing threatening letters.
Use red ink normally as long as you don't write someone's name. There is no taboo about using the color red normally.
Use red ink when signing a document with a seal. In Korean culture it is common to carry a small carved seal with your name on it. This seal is used to sign important documents such as banking forms. Because red ink is used in such occasions, this is one time when it is acceptable to record a name in red ink.
Do not write someone's name in red ink if they're alive. It can be regarded as a threat or an omen that they will die soon. If you're teaching, ensure that you don't write your students name in red on the class board or on one of their papers. If you give someone a gift, it's especially rude to sign their name in red on the card.