The First Quarter Day (established 2017) is a day to celebrate having survived a quarter of the new year. It takes place on 18 Discord and can be celebrated by paying for everything in quarters. Or you could make an offering to Eris of a quarter tossed into the nearest pool of water. She will be there shortly to take your offering and grant you your wish for an exciting year.
Second Quarter Day is on 37 Confusion, also known as Mid Year's Day to some Discordians.
Third Quarter Day is 55 Bureaucracy. About this time of the year, stores are looking forward to various holidays and have by now put their merchandise out for people to buy. The epitome of shopping holidays is known in the United States as Black Friday, established to be the day after Thanksgiving. Sit back and enjoy seeing everyone running around, trying to get stuff together for the holidays.
Fourth Quarter Day (Hole Day) is on 73 The Aftermath and is spent appreciating that you have a nice, full year in front of you. Then realizing that it is ,in fact, an empty year ahead of you.
Consult your pineal gland for more details.