Here's how to manually reassign leads.

Once you've received an email about the new lead, you can navigate directly to the lead record from the email notice.

On the lead record you can update who the lead is assigned by clicking on the name of the current assignee in the top right corner of the page:

The person the lead is assigned to will get an email notice that looks like this:

The ability to reassign leads an admin permission that can be granted to non-admins via the permissions page.