What is usually the next step after showing the VC dimension?
A distinction should be made between constructing practical machine learning algorithms and theoretical algorithms, such as PAC learning algorithms. A machine learning practitioner doesn't usually invoke the concept of VC dimension &mdash; indeed, many of them probably have never heard of it, especially if they're applying machine learning in some other subject. While VC dimension might be useful in coming up with algorithms (as in the case of SVMs), it appears to have no practical import.

When constructing theoretical algorithms such as learning algorithms under the PAC model, the story could be different, but unfortunately I don't know too much about that. From the little I've seen, VC dimension doesn't get mentioned even there. In fact, it seems that VC dimension is mentioned mostly in literature attempting to relate it to other parameters.