By far the fastest and easiest way is to do a reverse image lookup in Google.
Here's a link to Google's Search by Image functionality:
Google will look for similar colours, shapes, and patterns in other images across the internet. Although it may find images that aren't logos at all, this is the quickest way to begin.
Past that, you can post in graphic design communities as Whitcomb suggests.
Here are some great communities that will give you the feedback you're looking for:
Brands of the World - http://www.brandsoftheworld.com/
Reddit Logo Forum - http://www.reddit.com/r/Logo_Critique/
Starting with Google and then transitioning into conversations with actual people, you should be able to cover your bases pretty well.