How to send a SMS or MMS from a servlet?

There is no standard way for this. If you've studied the infrastructure for SMS (or MMS) messaging, you would've noticed that there needs to be a gateway for sending the SMS (or MMS). The API with which you ask the gateway to send a message depends on the gateway vendor.

I'm not aware of an open-source SMS gateway, but you'll find some commercial products with Google.

Oops. Actually there is one that I know of: www.kannel.org