3d dynamic pathfinding

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I would like to implement some method of dynamic pathfinding.

Say I have EntityX and I want this entity to navigate to PointXYZ - the path created should be totally dynamic, as my scenery is liable to change at all times. Also, my level mesh is treated as one big object, so it has polygonal collision, so the pathfinding needs to take this into account (to navigate succesfully around objects such as furniture).

Ideally I would like to be create a linked-list of nodes for the character to follow as the shortest path from their present position to the target.

What is the best way to go about this? I know absolutely nothing about this stuff!