Creating a navigation mesh 2D

I'm trying to create (implement) a navigation system… I want to be able to place various rectangular polygons (not rotated) and make a unique shape out of them (union). I'm having trouble though coming up with an algorithm to do it. I guess I want to end with a list of consecutive points that represent the shape… then I need to break those into triangles and lastly use it in conjunction with A*.
So my main problem is creating the Mesh and splitting it into triangles.. I'm working from scratch here so no external libraries :( just wanted …