There are two fixed points in this mechanism -- the servo crank, and the guide block that will constrain the slider (otherwise it could flop all around!) -- we'll use cardboard to build the structure.
Start with a corrugated cardboard box, such as a medium shipping box.
Mark the servo base onto the box using a pencil or pen. Keep the markings very close to the true dimensions of the servo, so that you can cut a snug opening for it to press fit.
Use a hobby knife to cut out the servo opening. It's best to use a metal ruler or straight edge to guide the knife edge.
Insert the alligator clip wires into the opening, then press the servo body in.
Now that the servo is fixed in place, we can determine the best position for the guide block.
With the crank rotated fully counterclockwise to its stopping point (180 degrees on the servo) extend and straighten the linkage as shown. Mark the top and bottom of the slider onto the box using a pencil or pen.
These two marks are where you will build up a small cardboard platform the rest the slider, and then two walls of cardboard for the upper and lower guides.
Place two more piece of cardboard like guide rails on the upper and lower "walls" of the stack. These should guide the slider, but not impede its motion.
Now, you can reconnect the alligator clips to the CPX as shown, by running the wires up from inside the box to the edge. Or you can poke a hole in the cardboard wherever you like -- that's one of the great features of cardboard!
Connect the battery pack to the CPX as well, using the JST connector. You can mount the battery pack inside the box with some tape.
Turn on the battery pack's power switch and away we go! Move the slider to chose between automatic or manual mode, where you can press the A and B buttons to actuate the slider.
You can mount the Circuit Playground Express to the box with a loop of masking tape, as I've done here, or get more creative using bamboo skewers as rivets, pipe cleaners, or double stick foam tape!
With the slider crank mechanism under your control you can now find some creative uses for it! You could attach a puppet, make a primitive train, or perhaps a lumbering box robot! Now that you have the power to convert rotation to linear motion, what will you make?