There are two basic techniques - either you could grant them access to your database to connect using its own protocol (for example, MySQL), OR you could provide an RPC service for them.
The advantage of granting them access is that it requires very little setup work for you - but there are many issues, including security.
Also, if you want to refactor your database, you'll then break all your affiliates' applications.
Normally providing a machine-readable feed is the way to do this.
Mark