English question, please help?

The first one is present tense, and I would use it to someone whose day has not ended yet.

The second one is past tense, and I would use it at the end of the day, or the next morning.

Both are correct but depends on when you are using it in the day. Former generally in the first half and later one in the second half

Both are grammatically correct, but also have different meanings.
-"How's your day?" means "How is your day?", which refers to the present tense.
-"How was your day?", however, refers to the past tense.

Ok, that's all I know. If you need extra information, google english grammar rules. Good luck.

"How's your day?" -- "How's" is a conjunction of "how is", and it is in the present tense. You would ask this to someone if you wanted to know how their day is at the current time

"How was your day?"-- This is in past (imperfect) tense, and you ask this to someone close to the end of their day, in order to ask how their entire day was as a whole.