how do I share an excel file using the internet?

We are a small horse training/breeding operation with 2 locations, one in
Texas and one in Tennessee. We send horses back and forth and would like to
get away from trying to keep up with the horses' health records using paper.
Can we put a spreadsheet out on the internet for both locations to enter
their information and have current information all of the time?

It can be done, I would grab a book at the store. I know how to upload an excel document to the internet but not sure how to make it "two way"