I use the professional versions of the product on the link below. It will create a slightly glossy surface, so if your table is dull, you need to either adjust the sheen or use a different product.

There are many solutions. Everyone seems to have a favorite. Here are frequently offered ones, in no particular order. Note that some have potential to cause unintended consequences.

Heat
Gently heat the area with a hair dryer to see if that drives out the moisture.

Mayonnaise
Smear mayonnaise on the spot, cover with plastic wrap and leave sit overnight. The next day, clean off and see if the spot is gone. It may require a second application. Some people report similar results with peanut butter or Vaseline.

Stain and ring removal cloths
Paint stores carry a yellow felt cloth that contains oils and a light abrasive. With rubbing, the oil displaces the moisture. Clean off the oil when finished. This may raise the sheen on flatter finishes.
A similar approach is baby oil and cigarette ashes, gently rubbed in.
Blush Remover / Blush Eliminator
Professional touch up technicians have an aerosol available that's lacquer thinner in a can. Spraying on a light coat dissolves the lacquer and gives the moisture a chance to evaporate away before the lacquer sets back up. This is for lacquer finishes only.
On mild cases, you may get a similar result by spraying on a light coat of aerosol lacquer, which are heavy in solvents.
Denatured alcohol
Gently pad a denatured alcohol dampened cloth over the spot in a sweeping motion. The alcohol is miscible in the water and they should evaporate away together. This is very effective on shellac finishes, but the alcohol is a solvent for shellac, so go gently. Aged lacquer is also susceptible to alcohol.
Proprietary products
Finish revivers such as Howard's Restor-a-finish can sometimes be effective at removing rings. Some of these products have methanol (an alcohol) or light mineral oil in them.
If the finish is flaking off (lost adhesion), you will have additional problems and a more extensive repair or refinishing will be in order.

Here is a link that might be useful: water ring remover

To Get Rid of Water Stains:

Method #1

• Form a paste with equal parts water and baking soda.
• Rub the paste onto the affected area in circular motions until the stain is removed.
• Wipe the surface clean and dry after.

Method #2

• Apply petroleum jelly and let it sit overnight, wiping it off the next day.

This blog covers maintaining wooden furniture and is where I sourced this information and infographic from, feel free to look into it!