There are several ways you can cut a hexagon from a sheet of paper. The most accurate would be to use a template, but if you have different sizes of paper, you would need many templates. Instead, I like to measure out the edges and cut hexagons individually from sheets. For precision, an Exacto-style knife and ruler on a cutting board, or a paper trimmer with a sliding blade, are the best ways to cut the edges, but scissors also work.
Depending on the size of sheet, there are different methods for cutting out hexagons accurately and efficiently.
For squares, I've tried several methods but my favorite requires a 30ยบ triangle ruler (along with a normal straight edged ruler) to mark the edges.
For rectangles, as long as the rectangle is wide enough, you can cut out a hexagon with just a few reference folds, no tools apart from cutting tools needed.