By using @api.onchange or @api.dependans

Thank you  Sehrish for your answer.

The problem when using your suggested approach is that currently when I click on any item in the o2m list a form pops up showing the clicked item's data instead of simply being selected. Onchange does not get triggered in this situation.

How can I stop this behavior?

According to my understanding about your question.
For this question: Then how can I trigger some method in the model passing the ID(s) of the selected item(s)?
you can create a onchange method. When you select some record using (m2o, o2m) than onchange method triggered.

    @api.one
    @api.onchange('the_field_which_you_have_selected')
    def onchange_your_field(self):
        #do something

Hope this will helps you.

Reference: http://learnopenerp.blogspot.com