I have a Topeak handlebar bag that has a clear plastic envelope that I put the cue sheets into. However, the envelope isn't as wide as a Letter or A4 size sheet of paper, and I either:
a. Cut the sides of the sheets of paper to fit the envelope or
b. If the cuesheets are issued before hand, and because the type is usually SO small, I transcribe it (either by computer or by hand) on to smallish notepad-sized paper.
If you don't have a handlebar bag, then there are various ideas out there on using (bulldog) paper clips around shifter cables or fitted to the handlebars, and ziploc bags, or specially shaped spokes that fit to the handlebars, too.
If you use a bag, arrange the paper inside so the leading edge on your handlebars is the bottom of the bag... that is, the opening is on the trailing edge -- that way, you won't get wind trying to open it, or worse, more rain than necessary working its way through.
My handlebar bag arrangement is far from perfect. I have to fold cue sheets in half to fit them lengthways, and I cannot simply turn the envelope over when I get to the fold because it is held to the bag by a Velcro strip. The plastic envelope also severely reflects light unless the light is form a certain angle.
The problem is a bit more annoying if there are a huge number of instructions over a short distance, say to get from the start to outside a city's limits, or worse, getting to the finish when you are tired and wet and cold and hungry! The problem is less so on rides that go straight out and straight back.
I will probably experiment with using just a plain ziploc bag and paper clips this coming season. The ability to simply flip the envelope is a much more attractive idea.