Set up a "good" audio system:
Start with a decent room (not tiny, not cubic, not weird shaped) that you have at least a degree of control over (time to yourself, can setup seating/speakers where best sounding, sound isolated if house is occupied while listening). If you can't achieve all this seriously consider headphones.
Set an overall budget.
Try to get out to shops, shows, and clubs to develop ideas of what you like (vinyl, streaming, rips, solid state, tubes, various speaker types - which can be a very personal decision) within your budget.
Gather a sampling of your favorite music that represents a wide range of what you typically listen to audition with. Note that the best music to judge by is live/unamplified music, otherwise you're just comparing yours versus theirs, as opposed to comparing live (real) versus whatever system you're listening to.
Limit auditions to no more than 4 systems/speakers per day but take your time with ones you're interested in (this will avoid listener fatigue). And take notes (avoid aural memory loss and forces you to really listen).