I remember the first time I tried mapping Q-space with pen & paper back in the early 90s. One of the first things I did upon downloading UQM (besides sacrifice a virgin to the developers) was to download a proper map. These are Good Things to have.
My database project includes a checkbox on the Hyperspace map labelled "Use Quasispace". Selecting a star with this active and moving to another star (preferably one far away) will activate the Quasispace map within. It will show you the shortest path through Quasispace to get where you're going (including which portal to take and what path to take when emerging from said portal).