Insert the tip of a marlinspike -- the metal, pointed spike you use for rope work -- under the end of the caulk between the teak deck planks. Lift the end of the caulk and pull it from between the planks. Repeat until all of the deck caulking is removed.
Remove the screws from the plank closest to the right, or starboard side, of the boat, with a screwdriver. Place the screws into a bag for sake-keeping. As you remove the screws that hold the plank in place, remove the teak planks from the boat. Measure and record the length of each plank with a measuring tape. For example, record the location from which the first plank was removed as "No. 1." Remove the screws from the adjacent plank. Remove, measure and record that plank as "No. 2." Repeat until the teak planking is completely removed.
Use a chop saw to cut replacement planking to length, using the recorded notes regarding the length and location of each plank. Move all of the replacement planks onto the boat.
Place the No. 1 plank on the boat and secure it in place with the screws you removed from the previous decking. Continue to replace the planks in order. Finish the planks to your taste, either with teak oil or varnish. Caulk between the planks with polyurethane caulking.