Custom Fieldtype in a plugin at user profile save
The best approach is probably to use the onAfterElementSave hook available to custom fieldtypes. Here's what that could look like (the following method should go into your custom fieldtype class, e.g. myawesomeplugin/fieldtypes/MyAwesomePluginFieldType.php):

public function onAfterElementSave()
{
    $field = $this;
    $fieldId = $this-&gt;model-&gt;id;
    $fieldHandle = $this-&gt;model-&gt;handle;
    $element = $this-&gt;element; // This is the UserModel, in your case
    $fieldContent = $element-&gt;getContent()-&gt;getAttribute($fieldHandle); // This is the content for the field

    // Do something awesome with the data above
    ...

}