You want dynamic nested model forms.
Here is a gem that makes it work out of the box
Note: you will need to use jquery or prototype javascript frameworks.
One of the most common gotchas:
Make sure the parent model has attr_accessible :children_attributes.
Example: School has_many :students, you would need attr_accessible :students_attributes in your School model
You can read up on this and more at RailsAPI page for accepts_nested_attributes_for