Shortest path form node X to nodes A, B, C in graph
Use BFS, and keep prev pointers.  Good textbooks will have a chapter on shortest-path algorithms where they describe how to reconstruct the paths themselves (not just the distances) using prev pointers; use that method, and then you'll be able to reconstruct a shortest path from $X$ to any other node.  Initially the estimated distance to all nodes is $+\infty$.  Whenever you update the distance to something lower, update its prev pointer to point to the node where you came from.