Would I have to conduct an experiment to write a scientific paper? I recently got a book named How to write and publish a Scientific Paper by Robert A. Day and Barbara Gastel. The book doesn't really explain the "background" of a scientific paper.  Would I have to conduct my own, original experiment in order to write a scientific paper, or could I just use the data from other experiments to make an orignal claim?
A scientific paper doesn't necessarily have to be based on an original experiment. You can write a paper that's a review (whether systematic or just comprehensive literature review) of the current body of literature for a specific topic or a meta analysis. You can also write papers that are derived from original experiments that you ran or secondary analyses of data from experiments run by others.

It depends on what the purpose of the paper is. If it's to introduce an entirely new phenomenon or theory, original experiments are pretty common. If it's to argue that current theories or concepts may be flawed in certain ways or you want to add something to existing literature, then meta analyses, original experiments, and secondary data analyses can all be relatively common and appropriate. If it's to introduce a new perspective to a theory or concept, then comprehensive literature reviews may suffice. This can also depend on what field you're in, so consider what the norms are in your field and whether the journal you want to publish in accepts the specific paper type.