There are two ways to get a satin (matte) finish—that is, a finish with less shine and reflection than gloss: rub the finish with abrasives or use a finish that contains flatting agents. There are pros and cons to each.
The easier of the two, by far, is to use a finish that contains flatting agents, usually labeled satin, matte, flat or semi-gloss. The terms are vague approximations of sheen (amount of shine or gloss) you will get. Some manufacturers selling into the professional trade use a numbering system to indicate sheen, with 90 being gloss and 10 being very flat.
Rubbing with abrasives is much more time consuming because you have to sand and abrade through a number of grits. Usually, you begin with fine-grit sandpaper, then advance through several abrasive powders, such as pumice and rottenstone, or rubbing compounds.
So rubbing can produce a much more perfect finish than using a finish containing flatting agents, but rubbing also creates a fragile finish. To reduce the likelihood of scratches showing, apply a paste wax or a furniture polish that contains silicone to the surface. Most aerosol furniture polishes, with the exception of Endust, contain silicone. They are very effective at reducing scratching and they usually make the wood and finish look deeper and richer.
Rubbing produces a much more perfect finish, with no flaws if you do it well, and with a much more pleasing soft, silky feel. This is good, and the extra work is often worth it for tabletops. But rubbing, by definition, leaves fine scratches in the finish. (It’s the scratches that create the lower sheen by reflecting light randomly.) And the scratches show marks easily when objects are moved on the surface. Even lightly dragging the back of your fingernail perpendicular to the polishing scratches will leave a mark.