It appears Google has recently changed it so that everyone gets up to 15GB of storage divided between GMail and all the other apps such as Google Drive, but images below a certain size (800×800 pixels if you don't have Google+) are mentioned as not counting below your storage limit. However I uploaded a bunch of 500×500 images as a test and they are definitely counting against the limit. A bit of further research suggests pictures uploaded by Google Drive are counted, although I couldn't find why this is since the same images when uploaded by Picasa Web are not and they are both going to Google.
I also have read that Google Drive images can be shared with Google+, although there is no mention of whether or not or how the small image exclusion works there either. But it also seems to be suggested that Google+ pictures up to 2048×2048 are also not counted against the limit, so I'm confused about how this works if you send the pictures for Google+ via Google Drive.
At the moment I only have Google Drive – the desktop client – I do not have Google+ or Picasa. That's the way I would like to keep it unless it's absolutely necessary to have one of the others in order to get unlimited small image uploads via Google Drive. Do I simply need to sign up for Google+, and then small images uploaded via Drive automatically stop counting against my storage limit, or do I have to add the step to share them with Google+, or do I have to actually use something outside of Google Drive to upload them, meaning I don't have the easy of seeing the pictures on my desktop and have to go through the web interface?
Update: Ok, it appears that Picasa Web has been transitioning to Google Photos which is really Google+ Photos, although I still only see my pictures in Picasa Web as I haven't "upgraded" to Google+.
Best Answer
According to a Google rep I talked to, the answer to this question is, "you can't". Any images in Google+ that don't count against your storage limit will as soon as Google Drive can see them.