Take immediate action.
Get several white cotton towels or paper towels. I prefer the cotton towels. Fold it over in half and then once more into quarters. Place the towel over the wine spill and press, allowing the towel to absorb as much of the wine as possible. You can even use your toe to press and use all your body weight to press the clean white towel onto the stain. Keep repeating. You may need more than one towel and lots of towels if the spill is big. Keep pressing to absorb the wine until you do not see any more color showing on the towel. Once you have removed all the wine possible, the next step is to get a glass of ice water. Dip a corner of a folded clean towel into the ice water and now blot with the ice water. This will help to dilute any red wine left. Do not pour water onto the carpet, as that will drive the wine deeper into the carpet. You want to pull out the wine, not drive it deeper. So continue with the ice water, being careful not to rub or scrub the carpet fibers, just press and blot. Scrubbing abraids the fibers and can ruin them. Go until you can't see any sign of the red wine. Now look around and see if there are any splashes of red wine that you may have missed. Repeat for any other areas you may have overlooked. Make a note of where this happened on your carpet, so the next time you have your carpets professionally cleaned you can be sure to point the area out to your carpet cleaner. She will be sure to get any residual stain out.