Playing on separate computers?

Hey guys, I recently purchased minecraft, and love it. -But, I was wondering how is it possible to play my world on different computers. On my home computer I have my main file, but at school computers and other laptops it doesn't have my saved data. --Would I have to get a copy of my save files or something to play it on other computers? Or could I maybe upload my world and make it only private to myself?

Thank you!