Take the equivalent of a large teaspoonful, about 5-6ml. Try two simple comparative exercises with a good-quality wine such as a Gewurztraminer or Sauvignon Blanc.
Take a sip and swallow it straight down. Take another sip, but this time work the wine well round your mouth for a few seconds (this is called "chewing") before swallowing. Notice how much more of its flavour you can taste.
Take a further sip and "chew" the wine well before swallowing a little and spitting out the rest. With the next sip of wine, in addition to chewing it, purse your lips and suck (not breathe) a little air through the wine two or three times before swallowing a little. Notice how you can taste/smell even more of the wine this way because you have deliberately "volarized" (released) its aromas. Always "chew" and "aerate" for several seconds to get the most out of any wine you are tasting.
Winetasters spit simply in order to stay sober when assessing large numbers of wines at one tasting.