How would one navigate interstellar space?

You would use the stars as your reference. Of course, some stars are more suited to this than others. For example, the Voyager Golden Records had pulsar maps, that in theory some alien civilisation could use to locate Earth (what could possibly go wrong?). So, stars with unique and easily recognisable characteristics make good 'landmarks' (in particular, pulsars).

For interest, you could also use pulsars. I belive the idea here is that pulsars have unique and well-defined pulse times along with being bright, so you could use them as natural GPS satellites.