Are you using scripts yet? If not you'll want to check out the information
here.
I would recommend
this script for keeping track of the HITs you've done. If you're using Hit Scraper, it will connect with that and show little boxes next to each hit so you can quickly see if you've done work for that requester and also if you've done that exact HIT's name before (though it
could be a new survey) More importantly, it will give you the ability to search your work history by adding a section below your normal mturk dashboard.
That being said. Many requesters will use some way to prevent retakes on their surveys i.e. using your ip address, assigning you a qual, or other means. Neither of these thing will help you 100% of the time, so being honest when you think you remember having done the survey before is pretty much your last line of defense.
I'm assuming here that you know that most tasks that are not a survey are termed 'batches', those you can do as many as you can stand unless it explicitly mentioned a limit in the instructions.
Hope that helps!