The A star or A* algorithm is a widely used, very effective pathfinding algorithm.
I made an application in Processing that is based on the implementation given here:
Here is a video of the application in action:
You can try it out with the desktop application here:
Windows 32 bit:
Linux 32 bit:
Android app here:
If you struggle to understand the tutorial, I have made a video that goes step-by-step through the algorithm: