You will need:
a piece of wood large enough for your chosen models to stand on
fabric scraps (some thicker material, some thinner/stretchy)
a glue gun and/or sewing materials
nails of various sizes, depending on size of models
cardboard (for larger model sizes)
Step 1: Cover the base with fabric
Cut out enough fabric to cover the top and sides of the wood. Place the wood face down on top of the fabric. Put a line of glue along the edges of the bottom and attach the fabric. Make sure the glue dries flat so that the board will be level. One way to achieve this is to glue and then flip the wood over and weight it.
(This step could probably be done by a staple gun, sewing, or other ingenious method. I just happen to have a glue gun).
To fasten the edges of the fabric, fold it as you would gift wrap and glue down. (You can see this better in the larger scale photo with the white fabric).