Best way to send anonymous email like craigslist

This is usually done by piping an e-mail address (often, a catch-all address) to PHP. Here's a tutorial on doing it that should get you started in the right direction.

The most probable solution is by doing what they called as Email Piping.

They insert the ad with an identifier like this:

*job-fepsd-1120347193*

alongside with the real email.

Then they receive the email by piping it to a PHP script. You can check Google for PHP and Piping where you will find good resources on the subject.

The script then searches for this Unique Identifier and associates it with a real email.
Then it forwards the email received to the real person.

There is also another possible solution (but less possible), they might be using POP3.
Then they would just make a check every X minutes on a catch-all address and then forward the message to the right person.