Note: Now that Workflows are live in all accounts, you can do everything that Triggers and Campaigns do (and more!), all in one builder! Click to learn more about Workflows.
In order to send new Membership signups a custom email with their login credentials, you'll want to first turn off the automated email that goes out:
Then you'll want to build a Trigger with the "Membership New Signup" condition on the left side and the "Send Email" action on the right side using Custom Values shown below.