I see people hold them cupped in the hand, by the stem and lately I see many people holding just the base pinched between thumb and curled finger.
I expect that there is some form that is considered proper, but don’t know if it depends on the type of glass, or type of wine (cupping white wine would warm it, right?).
I mainly hold the bottle by the neck, wipe the rim with my sleeve and pass it on.
-Tcat
My understanding is that if the wine is chilled, it should be held by the stem so you don’t warm it up with the heat from your hand.
Technically, it’s proper to hold the glass by the stem or base to keep from warming the wine. I’ve seen it held the way you described and (by French wine tasters) by cupping the base in the hand.
Usually, though, it’s only the utter wine snob who bothers with this.
I always hold my glass by the stem, whether it’s white or red wine. It’s commonly thought red wine can be as warm as it comes, but (if you want to get all wine snobby), in hot rooms it should be chilled before serving. Wine shouldn’t be served at near-body temperature, which is what it will quickly become if you cup the bowl of the glass in your sweaty palm.
OTOH, if wine which is served too cold (like in some restaurants which insist on nearly freezing the white to disguise its taste), you could use your hand to warm it up a little.
All such difficulties are of course avoided if you quickly knock it back your wine in one go. 
Since this is a wine thread, I’ll voice my pet hate: people who insist on uncorking wine five minutes before serving “to let it breath”. Wine is not going to breath in five minutes if it’s left in the bottle. There’s hardly enough surface area of the liquid exposed and only a small flow of air into the bottle. If you want to let the taste develop, pour the wine into glasses or a decanter. Otherwise, don’t bother with this fussy ritual of uncorking a few minutes in advance. It’s just silly.
First, make certain the jelly that came in the glass when one bought it has been thoroughly rinsed away…
Glass? Ppfftt…I drink it straight outta the box.
Stem end down.
Clenched in my fist as if it were struggling to get away.