There are many good articles here on Headfonia. You could click on Buyers’ Guides and read through those, then click on the Headphones topic header for each individual report. The “process” you go through is learning your own sound preferences, then matching that to the products that are available. It is a process, so you have to learn the major differences. Any shortcuts you take might be OK, but when you buy something that you discover you don’t like, make sure you can return that item.
One thing I suggest to prospective customers for a specific headphone, if I have that headphone on hand, is for them to suggest 2 or 3 music tracks by a particular artist and composer that I can sample on that headphone, not so much for me to suggest how it sounds, but mostly to check if that headphone has any real sonic issues with that music. For example, a headphone that’s ideal for classical and acoustic music might sound too harsh with metal and industrial goth.
While the data signal containing Bluetooth audio is compressed, headphone and earphone manufacturers have found ways to enhance the signal to compensate for its deficiencies in a way that even audiophiles can appreciate. We've included some wireless options here, but if you're really keen on cutting the cord, check out The Best Wireless Headphones. And if you want to go completely wireless (with no cord at all connecting the two earpieces), check out The Best True Wireless Headphones—just keep in mind these are about as far from over-ear headphones as you can get.