It depends on how big the stains are and what they are.
If the stains are larger than 3 or 4 inches in diameter it may take a few hours to remove them.
If the stains are just liquor and other common household stains you should be able to remove them.
Here is a method i have used for smaller stains on my pool table:
Take a small amount of vinegar and dab it onto a wet cloth. You can then rub the spot where the stain on the pool table is. Try this for a few minutes and see if the stain starts to come off. If the stain does not come off you will need to try something a bit stronger to remove the stain. The next suggestion is to get a little bit of baking soda and rub it into the stain. You will not want to use a large amount of baking soda. Just a small dot will be enough to do the trick without leaving a permanent stain on your pool able. If the stain is still not coming off you may just need a little bit of elbow grease. Once you have rubbed in the baking soda well, you can wet your cloth in warm water. Squeeze the cloth out well and then continue scrubbing the area for another five minutes. Follow the same procedure rinsing the rag out and rubbing the spot until all of the baking soda is gone, and the stain is removed.