Generally, formica & other plastic laminates are cut a little big, glued on, and then trimmed. This is because the glue used is a one-shot item; touch the surfaces, and they''re permanently bonded. If you''re really careful, however,you should be able to shape it exactly right, apply the glue to the two surfaces (the top of the old counter and the bottom of the new) and position the new sheet precisely over where it needs to be and drop it into place. If there''s a straight fiddle edge against which you can position the new sheet, that may work well, or you can perhaps keep the surfaces separated by a couple of metal rods. (They''re less likely to break than pencils or dowels.) You pull the rods, the new panel drops into position. Use a fine, sharp crosscut or hacksaw to cut the formica and then a file to get the exact edge you want. Your library will have a good section of how-to books - Reader''s Digest comes to mind - that would be worth consulting.
P.S. Besides being heavy (and slow) granite tiles will be very exciting to cut to fit curves, and you''ll have grout lines that will trap moisture and grow things. Ugh!