I realise that I am unable to just use an image willy nilly from the internet, but if an image is uploaded to a site like deviant art, am I able to use it on my site (not claiming it as my own, but as a background image)?
Sites like deviantART, flickr etc. will usually include the relevant copyright info with the images, look for one or more of the following symbols:
I have to say flickr does this considerably better than deviantART, and will let you search images which you are explicitly granted permission to use. If the license isn't stated clearly you have to assume that you do not have permission, though you can always contact the author.
Often the license is attribution based, i.e. you can use the image (sometimes for strictly non commercial usage), if the author is acknowledged in a manner of their choosing. The precise wording is
Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
Whether that is the case will depend on the original image and will differ from image to image.
Legally -- In the US, creative works do not need a copyright notice to be protected by copyright. Unless there is text or mark along with the image explicitly allowing non-commercial use (assuming your website is non-commercial) the answer is no.
Morally -- It isn't cool to represent someone else's work as your own and it isn't cool to put another person's name on your website (i.e. if you are giving them credit) without asking that person first. Don't do anything you wouldn't like done to yourself (I always think, "What if BP Oil did to me what I'm about to do to this guy?").