When using JAVA, I'd create a class called Node, and have a String attribute for the path. Every node I enqueue in the priority queue, I'd the the node it's coming through + the previous path.

Maybe there is a better way, but that's how I do it.

Keep another array 'B', if you are currently in node 'v', when you want to update the shortest distance of a node 'u', write 'B[u]=v' , finally, to get the shortest path, start from the ending node, and go backwards in the array B until you reach the starting node :

int len=0;  
int v=end_node;
while (1)
{
     path[len++]=v; 
     if (v==start_node)
         break; 
     v=B[v];
}  

now you have the path (backwards)

What I did was maintain an array par[] and for each node,i, explored store its parent vertex in par[i]. Then to output shortest path, start from n and keep printing par[] values till par[i] is equal to start vertex.