Dijkstra's algorithm is completely trivial. It's a greedy algorithm; there's nothing more complex involved than repeating the same simple step over and over. You pick a starting node then repeatedly add the lowest-cost edge to a node you haven't already reached. It's harder to explain what a "node" and "edge" are than to explain how Dijkstra's algorithm works.

Many textbooks make it sound harder than that because they want to examine complex data structures that make various parts of that as fast as possible. But the complexity is the implementation of the data structures, not Dijkstra's algorithm.