일 is used with numbers: 삼 일 동안 계속 비가 내렸어요. It kept raining for 3 days. 날 is used without numbers, usually referring to a specific day. 그 날 정말 슬펐어요. I was very sad that day. 하루 is one day (24 hours) without specification: 하루에 세 번 샤워해요. I shower three times a day.

Both 일 and 날 means "day". 일 is Chinese character-based and 날 native Korean. 일 is generally not used by itself, while 날 is used both by itself and as part of other words. ex) - 일: 매일(everyday), 내일(tomorrow), 평일(weekday), 휴일(holiday), 일요일(Sunday), ... - 날: 그날(that day), 전날(previous day), 다음날(next day), 날마다(each day), 어느 날(one day),,... - 날이 밝다(a day breaks), 날이 지다(a day's done), ... 하루 (not 히루) means "a single day", emphasizing the 24-hour period as a unit. ex) - 하루에 한번씩...: once a day... - 하루 하루를 열심히 살다: live each coming day to the full.