Welcome.
Steps in "proper" auditioning of loudspeakers (speaking with tongue in check, in total would take several lifetimes):
1.) Learn about music (genres, instruments, theory, artists) and decide what you prefer
2.) Learn what sonic (audiophile) attributes you would prioritize
2.) Learn about basic in-room sound propagation theory as it applies to your situation
3.) Learn about basic speaker design theory (types, drivers, cabinet construction, power requirements)
In buying loudspeakers I recommend a two step process. First do a "fly-by" quick listen to dismiss the majority of speakers out there. Then when you're ready to seriously audition try to do it at home with your gear/room and take notes using the full range of your favorite genres. Listen to no more than 3 or 4 loudspeakers at a time. Shop loudspeakers first, then find an amp that will serve them well. Finally select the source based on convenience, level of computer skills, and amount of hands on involvement you want.
