Once you've set up your Google Site map there is really nothing more that you have to do. Google should now spider your site based on your settings (although there are obviously no guarantees from Google that it will) and your listings will be updated accordingly.
If you really want to keep on top of things you should check your priority, exclusions and update frequency settings from time to time as pages that were important when you set your Google Site map up will inevitably change. Some will gain in importance and others will become less important and it's highly likely that the frequency that you update certain pages will change.
Keeping Google up-to-date on these kind of changes certainly won't do you any harm at all, it may even do you some good, but do not feel you need to do this on a daily or even weekly basis.
To resubmit your site for re-indexing simply locate and click the ‘Resubmit’ link in the Google Site maps page (link shown below) once you have logged in, and then submit the path to your XML site map again.
Something else you might want to do is log into your Google Site map account at: http://www.google.com/webmasters/sitemaps/login from time to time and check to make sure that everything is still as it should be. If there are any problem you will see an appropriate message under the Status column on the Google Site map page that lists your site maps.