See a demo at http://www.briangrinstead.com/files/astar/
The newest version of the algorithm using a Binary Heap. It is quite faster than the original. http://www.briangrinstead.com/blog/astar-search-algorithm-in-javascript-updated Binary Heap taken from http://eloquentjavascript.net/appendix2.html (license: http://creativecommons.org/licenses/by/3.0/)
The original version of the algorithm based off the original blog post at: http://www.briangrinstead.com/blog/astar-search-algorithm-in-javascript I left it in because it may be a little easier for some people to understand, but if you are planning on actually using this, I would strongly recommend using astar.js instead.
If you want just the A* search code (not the demo visualization), use code like this http://gist.github.com/581352
<script type='text/javascript' src='graph.js'></script>
<script type='text/javascript' src='astar.js'></script>
<script type='text/javascript'>
var graph = new Graph([
[1,1,1,1],
[0,1,1,0],
[0,0,1,1]
]);
var start = graph.nodes[0][0];
var end = graph.nodes[1][2];
var result = astar.search(graph.nodes, start, end);
// result is an array containing the shortest path
var resultWithDiagonals = astar.search(graph.nodes, start, end, true);
// result now searches diagonal neighbors as well
// Weight can easily be added by increasing the values within the graph, and where 0 is infinite (a wall)
var graphWithWeight = new Graph([
[1,1,2,30],
[0,4,1.3,0],
[0,0,5,1]
]);
var startWithWeight = graphWithWeight.nodes[0][0];
var endWithWeight = graphWithWeight.nodes[1][2];
var resultWithWeight = astar.search(graphWithWeight.nodes, startWithWeight, endWithWeight);
// resultWithWeight is an array containing the shortest path taking into account the weight of a node
</script>