3-tab shingles are normally cut into thirds and used for ridge and hip shingles. Most architectural shingles require that you buy the matching ridge shingle. To remove, simply use a flat pry bar. Generally ach ridge shingle is held down by a total of 4-roofing nails. Just pry them off. New ridge shingles depend on the type being applied, but for 3-tab:
Cut into thirds; nail through the roofing cement on the shingle (normally 5-1/2 inches from the end; overlay the next shingle so it covers the nails (normally a 5-1/8 reveal). Continue the pattern to completion. Architectural shingles: nailing instructions are on the box.
If the ridge shingles are deteriorated, the rest of the roof will not be far behind. Plan on re-roofing in the next couple of years. Good luck.