I have a logo design idea that I've put together, how can I check if the logo or idea has already been used elsewhere?
The answer you probably aren't going to like....
A Trademark Search
See here -> US Patent office: Conducting a Trademark Search
If you are truly interested in ensuring a logo or brand is not in use elsewhere, you customarily hire someone to do a trademark search. There are attorneys which specialize in trademarks and patents.
This is similar to when you register a business name, a search should be performed to ensure you aren't infringing on some other business already in the same market.
You can do reverse image searching and all that, but really those will only placate your immediate gratification urges. Although in some cases that may be enough. These types of searches are in no way sufficient for legal means. They are merely a cursory examination of what may be on the internet not everything which may exist. There are millions of brands and logos which may very well not be on the internet.
But if you want to legally be certain you have a unique mark... you generally need a professional (customarily an attorney) to search for you. They know the ins and outs of any issues.
If it's a monogram search the letters on Google and see if they've been used before.
Upload your logo to tinyeye.com and Google's reverse image search to see if it looks like something that's been used before.
If you made it from scratch not copying anything you can be pretty sure it's yours, unique and safe to use.
If it looks possibly like another brand then you might run into legal trouble and could be told to take it down.