I normally don’t publish asks but this is long and may be helpful for others as well.
First, I check at the original source or in the notes if there aren’t that many. Otherwise, I use the reverse image search on Google. It’s the little camera in the search bar where you can paste or upload the image. TinEye is a similar site. Sometimes they have different results but Google seems to have more. Newer or more obscure images might not be on either. Also, the majority of the links direct to Tumblr, Pinterest and Blogspot without sources so you may have to weed through pages until you find the original source, if there is one.
Movies/screencaps are the worst to find sources for. Older art is fairly easy. Interior/exterior housing almost always goes to a ton of Blogspot links but the source is usually somewhere. Miscellaneous photos are hit or miss, sometimes they lead to Flickr.
Fashion related images don’t always show up since the ones posted on Tumblr are usually new, scanned or fairly obscure. Or at least those are the kinds I end up searching for. It’s easier to look up by model, magazine, photographer, designer or whatever. There’s usually at least one familiar thing in the photo for me and I search for that. The calendar option on Google Images works great while looking for newer images. TFS is another resource, they usually show up in the reverse image search though.
It’s possible not to find anything. I like to add what I do know (if anything) and tag with “source?” incase anyone else knows. I’ve had quite a few people tell me sources.