How is DHT different than regular hash tables in context to data/node lookup?
Your question in the first sentence is a bit vague and open-ended. I'm guessing you want to know about routing and mutual node knowledge in the context of lookup.

Each node shouldn't have to know about every other node. Assuming a hash ring topology, the simplest approach is to have each node know about its two neighbors on the ring. This defines a circular linked list. Unfortunately, as with all linked lists, it only supports slow linear search. It's also very sensitive to node removal: if any two nodes go offline, it breaks the connectivity of the ring.

If you try to repair this idea by having nodes maintain knowledge of their longer-range relatives then you eventually wind up with the idea of a skip graph, a generalization of skip lists that can handle node disappearance robustly. Unlike skip lists they are not explicitly stratified, which is important due to the non-hierarchical peer-to-peer nature of the problem.