Hire a Korean nanny and ask her to only speak to the children in her native language. Having someone spend the day with the children would help fast-track their language acquisition skills, particularly if they had to ask permission to watch television or play on the computer in Korean.
Contact the Korean cultural center nearest you and inquire if they offer any language classes for children. Even if they don't have language programs, perhaps they know of somewhere that does.
Find a Korean tutor. Ask friends if they know a native Korean speaker, put up a notice on the community bulletin board or advertise on the Internet. An ideal situation would be if he had children that could come along and play with your progeny.
Get Korean story books for your children. Ask the local bookshop to order them for you or go online to make your selection. A Korean alphabet book would be a good place to begin.
Insist the children only watch Korean television for kids. Try to create as much of a Korean immersion atmosphere for them as possible. Cartoon are particularly good for language acquisition, as they are designed for kids and frequently repeat the same words.
Check out the Korean language lessons and songs available on sites like YouTube. Decide which broadcasts are best and bookmark a list for the children to watch.
Encourage the children to share the Korean they are learning with you. Ask them what the names of things in the house -- chair, book, door -- are in Korean. Have them read stories to you when they have learned enough "hanjas."