moving to new computer

Hopefully I'm asking this question correctly, not being versed in the tech lingo used in these here forums. I got a newer used MacBook and I would like to transfer my Zotero stuff to it. I have many readings and papers that I'd like to keep track of for my profession. I vaguely understand that my files are stored on my computer, but accessible with synching. Is it possible to 'move' these things to my new computer and keep access to them, even after I clear the old one out and sell it? If so, could somebody explain how, as though you were explaining it to a half-literate vegetable with hands and eyes?
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