What is the process for obtaining a visa for college-aged children of expatriates in Thailand?

It's in the rules for extensions based on being the family member of a foreigner allowed here,

Clause 2.20 point 4: In the case of children, adopted children, or spouse’s children, said children, adopted children, or spouse’s children must not be married, must live with the alien as part of the family, and must not be over 20 years of age.