Wax paper straws are generally a thing of the past. Now, manufacturing of straws is mostly done with plastics. A plastic resin powder (mixed with additives like colorants) is first melted and made into pellets. (The pellets are easier to mold than the initial powder.) The pellets are dried and cooled, and then are off to another hopper, where they are again heated, to about 500 degrees F (260 degrees C), and melted into a liquid. The resin is extruded into the shape of a long tube, and might be pushed through by a counterintuitively named "puller" that helps it keep its shape as it takes a cooling water bath.
Crazy straws -- that is, the ones with loops and turns that resemble a wacky roller coaster -- will go through molding equipment before their water bath to get their shape.
Flexible straws with that accordion bend near the top are done a little differently. After the straws are cooled and cut, they're directed into trays with individual slots. Pins with rings carved into them are then inserted into the straws, and the pins move the products into parallel "jaws," that are clamped along the neck of the straw. The clamping of the jaws creates the corrugation for the flexible straw (without, of course, crimping the straw completely shut). Then off to packaging the straws go.
The industry seems to be moving at a clip; in 2010, Tetra Pak Tubex in Virginia made about 4 billion straws, and had plans to increase production speed even more [source: Blackwell]. But there's also greater interest in alternatives to plastic straws these days. You can easily find metal and bamboo straws, as well as bent glass straws, which are presumably molded to their L-shape when the material is heated. Don't attempt to straighten and unstraighten a bent glass one though, unless you want to break it.
Or you can go really retro and make your own wax paper straws. Just keep a screw and same dental floss handy, and voila -- your very own American invention.