Design for board to put on table to make it bigger?
It's a relatively simple project. While specific plans would need to be done using  the dimensions of the  table desired, it's very basic power-tool carpentry. It requires high precision, and the correct hinges, but isn't hard.
Essentially, you can just put the hinges outboard of the supporting table's width, on the underside. Let the table hold the panels up. So, if you have a desire for a 3'6&quot; wide, 6' long surface, but a 2' wide table, and need it to fit into your 3x5' trunk, you rip a board to 3'6&quot; wide, 6' long, then rip it to  two chunks 3' long. Finish the edges as desired, except the two which will face. Roundover the underside with a 1/4&quot; roundover, and mount standard door hinges (4&quot; wide) equally distant from the central table and the edge. (That should be 42-(2x4&quot; hinges)-(24&quot; central table)/4&quot; from edge - 1.25&quot; in from edge.) If being particularly fancy, you use a straight-cut bit and route out the hinges flush, so it folds truly flat...
If felting it, mount the hinges so that two compressed felt layers separate the two pieces, and the felt gets mounted so it covers the ends with the hinges. (This ensures that one only has a line between them, so stuff can't get under the felt easily.) also wrap it around the other edges.
Remember to both glue and either nail or staple the felt.
resource videos
Ask this Old House has a show that shows recessing door hinges. Uses a jig, two clamps, and a hand router. Or, alternatively, a wood chisel, and some patience. (if using engineered wood products, use the router.)
New Yankee Workshop, American Woodshop, Rough Cut, or The Woodsmith Shop all have covered hinges, as well.
advanced technique
If you make it thick enough, a Soss hinge could be used; their smallest one is 3/8&quot; and needs 3/32&quot; clearance on the folded-in side (and at least as much outside) for 9/16&quot; wood thickness minimum. It will, however, affect the felting. Soss hinges require skill at mortising, which is a more advanced (and past my level) skill.