There are slight variations in the custom for men and women. Men meeting for the first time usually shake hands only. However, male relatives and close friends will exchange a single kiss on the cheek. Kissing men on the cheek is in no way an affront to a man’s machismo. I have seen members of that uber-macho profession, the Policia, exchange a kiss in hello. Women, however, can kiss everyone. So, women kiss women and men; and men kiss women and close male friends and relatives. Got that?
The same goes for goodbyes. Just like my mother does in the U.S., much to the chagrin of my dad, when you leave a place you say goodbye to everyone individually. Not doing so is unthinkable. And of course, if you kissed them hello, you kiss them goodbye.
As for the kiss itself, it is a quick but sincere peck on the right cheek, not exactly an air-kiss and not a lingering pressing of lips to cheek – that would be icky. In Uruguay, they kiss once, not twice like they do in Italy.
Overall, Uruguayans are very polite, to each other and to foreigners. I think this kissing custom may have something to do with that. When a kiss is exchanged in greeting people, one is reminded of their humanity. There is less of a barrier between people and I think this makes them more considerate of others.

This is never okay, though, anywhere.
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