Coax one end of the table top away from the other until you have enough room between the two to insert a leaf. If you want to move both ends at once, you might need someone else to help.
Slide the leaf into the interval you have created.
Merge the table ends with the leaf by pushing in at either table end.
Measure your pedestal table for height and width.
Seek a table of of identical, or nearly identical, height and width. You may have such a table in your basement or attic, for example. Otherwise, you can look for one online or in furniture, department or big-box retail establishments. This second table does not need to be made of the same material as your pedestal table.
Find a tablecloth that is large enough to cover the two tables, once they are placed end-to-end.
Place the found table so that it abuts your pedestal table and lay the tablecloth across both tables.
Warn table users about the makeshift extension, letting them know the location of the gap between the two tables. Be sure to tell family, guests and serving help, if any, not to place any weight across the gap, as spills or injury may result.