Water dripping off the flexible hose beneath the sink indicates a leak at the hose-to-spout connection, the hose-to-spray-head connection, or somewhere in the hose itself. To repair the hose:
Step 1: Dry hose thoroughly, and check head connection. If leak is at this point, tighten connection, disassemble and make repairs, or replace head and hose assembly.
Step 2: Check spout connection under sink. Tightening may stop leak here.
Step 3. If leak continues, disconnect hose, apply plumbers' joint compound or wrap plumbers' joint tape around threads, and reconnect hose. The easiest way to spot leak in hose is to inspect it inch by inch under strong light while water is running through it. Look particularly for tiny cracks, chafes, or indications of some mechanical damage. Temporary repairs can be made by wrapping slightly damaged section of hose with vinyl electrical tape, but replacement of the hose will probably be necessary eventually.