Help understanding pathfinding

Before anyone answers I'd just like to express that I have checked out the unify example, the wiki for a*, angryant and arongranberg etc so please spare me the links

My problem is after reading through countless examples and explainations nothing seems to be sinking in. I understand the concept of pathfinding, you have a set of waypoints/nodes and you somehow work out the shortest route and take it (hypothetically) and i know there are many different ways of doing it.

I wondered if someone would be able to break it down for me and example step by step the logic of it and how i would go about implementing it?

What im trying to achieve is the standard enemy ai, move towards player avoiding obstacles.

Thanks in advance!