The -s on these words not only has a sound that our students need to learn, it also has a meaning they need to understand.
I talk about this aloud before showing the child the card. So, for example, say to the child something like, "I have one cup. If I have two of them, would I say that I have two cup?" If the child is academically ready for this sort of topic, he will say, "No!" And then you can say, "Well, what would I say, then? I have two -- what? What do I have two of?" And the child should reply with cup. (If he doesn't know, it is okay to tell him, just know that this means he's probably not ready for the idea.) So then have a similar conversation about dog and bug.
After the concept has been introduced like this, take out the binder card and go over the words. I use the words cup, dog, and bug.
Have the child read cup and remind him that this is singular -- one cup. And then show him how the s is added to the end to make it plural. Sometimes, this s is soft and says |s| and other times is is hard and says |z|. I actually teach my students to decipher the words in their singular form and then mentally make them plural before adding the s sound. How do they know which one? Well, if they already know the words -- and they usually do in early reading -- it will come to them intuitively, because they know how to say dogs, for example.
Most kids don't have too much trouble with this, and the difference between the hard and soft sound is so minimal that it's not a big deal. If they happen to get the sound incorrect, don't be afraid to simply say the correct sound in order to reinforce it. They'll get it in time.