No that is right, though this is not a quick process, binding just attaches the model to the skeleton and make certain assumptions on what vertices will be effecting when joints are moved. You now have to fine tune this binding by painting weights into your model which lets you control where and how joints bend.

I would try and find a tutorial on painting weights as it will be much clearer than me trying to explain from memory plus i've only done this a few times myself and am far from an expert.