Bread Box
#2

If you know the basic idea of how the box is to be. The door should be dowel rods spilt in half the long way, then placed on a piece of cloth with glue side by side. Route a groove in the side of the box the same size as the half of dowel and place the ends the grove so the door will go up and down.
#3

Dwight has a good idea, but, you don't need to go to the trouble of splitting dowels. Flat strips approximately 1/4" thick and 3/8" to 5/8" wide, (depending on how you want the door to look), glued to heavy fabric will work just as well. The bottom of the door should be a heavier piece, dadoed to accommodate the bottom strip and material (glue in) and should be slightly shorter than the inside dimension of the box (the flat strips should extend about 1/4" on each end, fitting into the groove cut in the inside sides of the box)
Good idea to chamfer the top edges of the strips, looks better.
Good idea to chamfer the top edges of the strips, looks better.