Update database table when pressing button

Hi, I’m sure there’s an easy solution to this but I just haven’t been able to find it yet.
I’m working on a plugin that lets you update a postID variable in a database table I created. I created an admin page with a <form> where the new ID can be entered and I want it to update the ID in the table when I press a button.
I know how to use the $wpdb->update(); function. My question is what needs to happen after the button is pressed.
Thanks!