Routing in Bitcoin Lightning Network
There's no document explaining step-by-step, because the routing decisions are not part of the protocol (the BOLTs). It is purely client-side decision making about how to find a route through the graph, and any client can choose to implement their own mechanisms. There is no compatibility issues because only the payer makes routing decisions, and intermediate hops merely forward packets as requested.

If you wish to know the specific details of how LND, c-lightning etc implement it, you will need to dig into the code and documentation for those projects.

As far as I'm aware, the current implementations all use a variant of Dijstra's algorithm, or A*, taking the routing fees as the heuristic to minimize when calculating the weights of each path, and c-lightning uses the Bellman-Ford modification in the link above.

Once a path has been calculated by the payer, there is a standard process by which the path and the packets for it are constructed, defined in BOLT#4.