Luckily there are plenty of remedies to get that shit out. All of them emphasize the necessity for rapid action and to always blot rather than rub, but otherwise there's no consensus on the most effective method. Here are the best seven that we found, but if we missed one be sure to spill a suggestion in the comments section.
Timothy DeLaGhetto and David So Hit Up the Taste of Little Italy Food Festival
The American Chemical Society doesn't seem like a likely advocate of pouring vodka onto the carpet, but the science is on its side. Apparently higher-proof spirits like vodka trump red wine by dissolving the color pigments and keeping them from clinging to carpet or other fabrics.
Instructables first soaked a cloth in red wine, then cut it in two and coated one in salt and submerged the other in milk. After an hour soak each, both were finished with castile soap. Milk firmly defeated its sodium opponent (though the salt did put up a pretty good fight!)
Harking back to when people actually kept this mixer on hand, club soda has long been reported to defeat red wine stains if you soak the fabric from back to front then blot like a maniac. But there's actually little explanation of why this works. Scientific American dug into the reasoning of why, but surprisingly the best it could come up with is that it might be the bubbles. Thanks for nothing, science!
Salt, boiling water, and vinegar cocktail
Here's a many-stepped method: soak with cold water, cover with salt (until it turns pink), pour on some boiling water, and then let the clothing sit in a vinegar solution before rinsing. It's pretty effective if you have the time.
Soak the stain in equal parts dishwashing liquid soap and hydrogen peroxide, then blot it up!
White wine and baking soda
To get stains out of carpets, first soak the stain in white wine to dilute the color, then follow up with a baking soda paste (3:1 soda to water). Keep that paste moist by spraying with water over the course of an hour, and the stain should disappear.