I'm building my own routing engine - which means I'm not using any of the routing frameworks for OSM.
So far I've built a graph with edges and vertices.
I'm parsing all the ways that are highways (I'm not taking areas).
My question is: how can turn a way into an edge (with one only two nodes, one defining the start and one defining the end) and remove all the ones in the middle? What approach has developers taken with this problem?
You could of course have a look at the existing routing engines which you don't want to use, each of which have solved that problem in one way or the other.
The question that you have been linked to in the post you reference above actually contains the answer. Re-read it: How can I convert an OSM XML file into a graph representation?
I was looking for an explanation that's a bit more low level.
Can you be more specific? Which parts are unclear to you? Where are you stuck?