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 and shape of the sheet, there are different methods for cutting out hexagons accurately and efficiently.
For squares, I've tried several methods but my favorite requires a 30º/60º/90º triangle ruler (along with a normal straight edged ruler) to mark the edges. This tool can be purchased at many art, craft, stationery, and office supply stores, in varying sizes (make sure it's large enough to cover the common sizes of paper you intend to cut.)
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.
For an alternate take on this topic, check out Madonna Yoder's video.