First get a cook book stand. I bought it at a shop boswells (UK) for 10 GBP.
Step 1: Remove screws carefully and disconnect the hinges.
Now turn the whole stand bottom up and replace the hinge on the inside.
Next, go to some hardware or DIY store and get a hinge. In the picture you can see it is the black metal one. I got it from a store called "wickes" for one pound (get two screws for it)
Now remove the small piece of wood that keeps the stand at a certain angle. In my stand it was fastened by a couple of spring. Replace it with the metal hinge. Try to experiment with the height you need before you fix it.