Use the built-in extension if there is one. Many dining tables feature a collapsible extension panel or a split in the center where leaves may be inserted to add seating for additional people--sometimes you can seat as many as 6 to 8 extra people this way. Follow the manufacturer's directions to expand your table.
If your table doesn't extend, or if you still don't have enough room, purchase card tables that are the same approximate width and height of your dining table. Set them up at either end of the dining table, and cover them with the same tablecloth to create an illusion of continuity. Just be sure your guests are aware that they might not be quite as stable as the regular table.
If your table is irregularly shaped or card tables prove too flimsy, extend your table with a large, sturdy board. Lay a tablecloth or other cover over the table to protect it, then lay the board down on top and cover with an additional tablecloth. If your board requires support on the ends, a barstool or other object of the correct height can be placed under the sections of the board that need support. Again, warn your guests of the arrangement so that no one accidentally moves the support or the tablecloth.