I don't know if I'm an "expert", but I've French polished half a dozen or so pieces of furniture with excellent results. I learned by scrutinizing George Frank's Article in FWW's "Finishes and Finishing Techniques" found on page 56. There are various schools of French polishing, I followed Frank's method which is supposed to be the true French one.
To start out, this tampon business. The tampon (with respect to French polishing) is a wad of wool surrounded by a tough exterior. I've used linen which is what Frank uses and had good success. Take a wad of wool about the size of a small egg and surround it with some linen. Draw the linen tight and twist it. I have several, one I use for the smoothing phase (which I'll discuss in a minute) and one for the bodying phase. Once you make these, don't throw them out. They are good as long as the linen doesn't wear through. An old pair of wool socks makes a very good interior material. I store the tampons in a pickle jar with a little alcohol in the bottom.
You'll also need some mineral oil, some 2 1/2 pound cut shellac, some 4F pumice, and Shellac solvent (I like Behlens since it has other stuff in it other than Methanol--remember all wood alcohol will destroy your optic nerve). I wear a pair of rubber gloves. I'm a hot sauce addict, I find the perfect thing to put these fluids in is a Durkee 12 oz hot sauce bottle. You have to add very small amounts of the shellac, mineral oil, and alcohol to the tampon and these are great for that task due to the shaker type top (which is removable by the way).
So to begin: Sand or scrape your top to final smoothness, and finish by sanding with 320 grit. The sanding is important, don't bypass it. Coat your top with a generous coat of mineral oil, and wipe off the excess right away. You'll have an oily darkened top at this point. Get the tampon you plan to use as your smoothing tampon, saturate the interior with only alcohol (no shellac), squeeze out the excess. Sprinkle a *small* amount of 4F pumice on the top, all over. Grasp the tampon and start rubbing the top--hard. Work in a random pattern and cover all the top. As the tampon dries out, peel off the outer wrapper and feed the wool with alcohol from your shaker bottle. Keep adding pumice as you notice it disappearing. What you're doing is jamming pumice (which is transparent) down into the open pores of the wood. It's sort of acting as a wood filler. The other thing you're doing is microsanding the top, making it as smooth as it can be. Any blemish that was in your top prior to the pumice will be magnified about 1,000,000 times and be quite noticeable. Careful preparation of the top is very important. Continue feeding your tampon, adding pumice to the top, and rubbing hard, in a random pattern. Soon you'll see frosted areas of the top start to appear. This is mineral oil being displaced from the pores and rising to the surface. This is good. Keep rubbing until you see this effect all over. This takes about an hour for a coffee table top for someone who is experienced. It might take as much as two hours for a first time. The main thing is to push hard on the top with the tampon, keep the tampon moving in a random pattern, and keep feeding the tampon with alcohol and the top with pumice.
At this point, take a break. Your fingers will be sore from all the pressure. Mineral oil doesn't evaporate so you can let it rest overnight.
The next time you work on it, get the tampon you intend to use for finishing. Saturate it with alcohol and start working on the top as before. The next time you need to make it wet, add a little of the shellac instead of the alcohol. Frank says to add alcohol too, but I don't notice a difference in switching over to shellac completely. Keep the tampon moving in a random pattern and continue to push hard. Keep adding small (2 or 3 drops of shellac) to the tampon. If the tampon starts to get dry, add only some alcohol, particularly is you have a lot of shellac on one area of the top you want to move around. You can't go wrong by using only alcohol. I generally go through a phase of adding shellac, switch over to straight alcohol for a time, and go back to shellac. It keeps the finish even. Continue to sprinkle on a very small quantity of pumice, sort of like adding salt between your fingers to a soup. No big piles, just a sprinkle.
Sooner or later the mineral oil you started with will get absorbed and the tampon will grab on the top. The solution is to add a small drop of mineral oil to the *OUTSIDE* of the tampon. This acts as a lubricant and stops the grabbing action. Since the alcohol evaporates so fast, the shellac hardens and grabs the weave of the tampon. The oil prevents this.
This may seem like a lot to track, but it becomes second nature after a time. Tampon grabs, add oil. Add shellac to the inside of the tampon routinely. Add only alcohol after adding shellac for a time. Keep rubbing hard, I mean *hard* and rub in a random pattern.
At this point you'll be able to see the shellac build up on the top. The frosted clouds of mineral oil will move around. This phase takes several hours.
Look at the quality of the top. If there are any craters, or rough spots, concentrate on that area by adding more pumice and shellac. At the end of this phase the top should be glossy, the finish as thick as you want it with scattered frosted areas. When it reaches this point, switch over to alcohol to feed your tampon for several times and give it a rest.
The third time you work on your top will be your last. Switch to a new tampon that hasn't had any oil or pumice added to it, only alcohol. Squeeze it out to just this side of dry (slightly damp) and gently glide it on the top. You want to gently remove the oil which is scattered around the top. The tampon will get dry, add small amounts of alcohol. The action is sort of like doing a spit shine on your shoes. Press too hard and you'll move around the finish. You want to soak up the oil, buff the top, and leave it at that. After about twenty minutes of light rubbing in a random pattern you'll be done. You'll use the lightest of strokes toward the end. What you're doing here is moving around the shellac in an even film. When you're satisfied--you're done. Allow your top to dry overnight, and follow up with a generous coat of paste wax.
Your top will absolutely gleam back at you. I like to do this on figured woods like curly maple, the result is spectacular. I don't think there is any value added for plain woods like oak, straight grained mahogany, etc.
For the rest of the piece, start out the same, but brush on the shellac and smooth it with an alcohol soaked tampon.
Legs and moldings have such small surface areas, they don't reflect the light like large flat surfaces which is where you want to spend your time. The good part is you can repair the top by going back to the intermediate stage if you have to.
Just say your forearms would look like Popeye's if you did this for a living