"Putting forth effort" means working, at least a little bit, to accomplish something.
You can use this phrase to react to someone who doesn't try hard at all:
Come on! You're not even putting forth any effort!
"Putting forth some effort" just means working a little bit, so you can use this phrase to decribe someone who isn't actually working very hard, but is doing enough:
Her class is super easy. As long as you put forth some effort, you'll be able to pass with no problem.