You could make the object a field in your form. When the relevant event fires from a control, then call the appropriate operation on the object.
Alternatively, have a Presenter/Controller object that stores your form as a field. It could take it as a parameter in it's constructor. This presenter can then subscribe to your form's relevant events and act appropriately. You could go further with this and extract an interface from your form and program to that in the presenter instead which would help testing. Have a look at the MVP pattern.