How do you sort your LPs?

By color! 
It's a thing we started in college with several room mates, decades ago.  Amazing how well it worked!  And still works.

Completely random.

bin for each genre, then by alphabet in each bin

Grouped by genre, then sorted alphabetically by name of band or last name of main artist. After that random within the band/artist. 

Last year I decided to finally organize my LPs and CDs.

The LPs are organized alphabetically by band name or surname. The real job was taking it one step further by inputting these albums, same way, on an excel spreadsheet. The spreadsheet has these columns:

Group / Artist,  album title ,  Label,  Label catalog # or UPC,  year of pressing / release,  LP condition,  sleeve condition,  size of media 10" or 12",  # of discs  and  speed (33 or 45).

My CDs are organized the same way and are done so on a separate storage rack system, except they currently are not logged into the excel spreadsheet (yet). Eventually, they will be on a slightly different list: 

Artist. album title, Label. Label catalog #,  year,  # discs,  jewel case,  digital or box set.

I had to resort to cataloging my LPs because I was buying the same music that I already have. In some cases I wanted a variety of pressings of the same albums, but mostly settled on one favorite.

It takes a lot of time cataloging your music, but it's nice to have these lists at your fingertips on your phone when music shopping!