You'd just submit the form directly to the auto action URL. An HTML form contains an action attribute, which is the URL the form will submit to. You'd simply supply your auto action for that attribute. In the context of BreezingForms I've no clue how you'd configure that as I'm not the developer of BreezingForms so I don't know how its forms are handled specifically. You shouldn't need to write a single line of PHP. Example form as follows.
Code:
<form action="AUTOACTION_URL_HERE" method="post">
<label for="name">Name</label>
<input id="name" type="text" name="name" />
<label for="email">Email</label>
<input id="email" type="text" name="email" />
<label for="username">Username</label>
<input id="username" type="text" name="username" />
<label for="password">Password</label>
<input id="password" type="text" name="password" />
</form>
This would work with the below for example.
Global
Triggers: None
Type: Registration
User: Self
Access: All Non-Registered Users
Action
Approval: Default (CB setting)
Confirmation: Default (CB setting)
Username: [post_username]
Password: [post_password]
Email: [post_email]
Groups: Registered
Name: [post_name]
Suppress Emails: No
You can add validation using conditions, etc.. there's a lot more than can be done here to improve for the form of course, but this is just meant to be an example.