Watch this video from This Old House to learn how to repair a kitchen sink sprayer.
1. Turn off hot- and cold-water at the shut-off valves under sink.
2. Loosen cap behind faucet's spout with pliers; protect chrome cap with a rag.
3. Remove cap and stuff the rag into the sink's drain.
4. Use a quarter to loosen the old diverter.
5. Pull out the old diverter and its rubber gasket with needle-nose pliers.
6. Wrap Teflon tape around threads of new diverter.
7. Carefully thread the new diverter into place; tighten it with the quarter.
8. Remove rag covering the drain.
9. Tighten the cap over the diverter using pliers and a protective rag.
10. Turn on the water, test the sprayer.