From the above, it appears to me that paulga is looking for advice as to how to take the faucet's handles off of the faucet, not remove the faucet itself from the countertop.
If so, in the case of the clear plastic knobs it could be that there is a cap at the top of each knob, about 1 1/4" in diameter that using a sharp knife you can carefully lever up and off which would expose a screw that once removed allows the rest of the knob to pull of the valve's shaft. It may take some gentle persuasion using a lever if the knobs have been on for a while.
With the white porcelain 4 spoke handles, look for a set screw somewhere between the spokes to unwind using an allen key or hexagonal bit socket. Once out, again lift up with gentle persuasion.
Once the knobs are off you have access to the valve itself, which in most instances it is easy to remove to old cartridge, clean the valve body and install a new cartridge.
You do all of this work from a standing position in front of the sink, no sore ribs, backache, pillows or profane language is required, unless you forgot to turn the water off first.
Also, there is no need to remove the faucet from the countertop.
Good luck, nobody likes a dripping faucet.