How to resvole source table fields having foreign IDs of other tables?

I've recently used DataTables to provide a user access to a MySQL-table which is access through an self-made REST-API from the table. This works pretty nice so far, but the accessed table has some foreign-IDs of some other tables in it, which i'd like to present als readable text to the user.
Is there a way to resolve the IDs in each record with a field (e.g. "label") of the foreign table, or do i need to create a special API endpoint returning that data as a result of a SQL JOIN operation?