Depends on the type of anasthesia used.
If you have a modern dentist you will get a simple injection in your gums to numb the area, after which the tooth can be removed painlessly. The anasthesia is very local and won't even cause uncontrolled drooling, just a numbness of the mouth that lasts a few hours.
If you have a dentist who for some reason still thinks it is circa 1950 you may get laughing gas (nitrous oxide) which can have much more serious side effects (including death), which is why no dentist worth his salt uses that anymore.
These days the removal of a wisdom tooth can be done quickly, cleanly and painlessly. My dentist always advises people to have them removed before they start causing trouble, because at that time they will still have the structural integrity to be removed in one piece and with one pull.
If you wait until they start to decay they may have to be removed in pieces, which involves making incisions into the gums.
The first procedure has you eating normally again one to two days after the surgery, while the second one may have you in pain for a week or two.
One thing to be careful of with wisdom teeth: When they are pulled they leave a relatively big hole in your jaw. This hole gets filled with a blood clot and that is normal and good. However, this clot may dislodge itself, leading to a nerve being directly exposed to air which is incredibly painful.
To avoid this it is very important to avoid svcking motions for the first two days or so, after that the risk of so-called 'dry socket' is neglible. This means no beverages drunk from straws or smoking. If you do happen to get dry socket (it is rare), plug the hole with a piece of sterile gauze and contact your dentist, stitches may be in order.
Plugging the hole will grant instant relief from the worst of the pain.