It is a common issue, white cloth and red wine do not go well together.
I was always told that once spilled, just cover the area with salt and all will be good. I have been fortunate that no one ever spilled red wine on my table (knock on wood!), so I have decided to make an experiment, to know what to do, just in case.
My granny once told be that milk was the better option, so lets see which was is the better to enjoy summer with and with out spills.
So let's start the experiment: Salt vs. Milk

Items used:
* red wine
* ordinary household salt
* ordinary FULL cream milk
* castille soap
* COLD water
* white cotton cloth

Let's get started ;O)

Step 1: Step 1: Soak White Cloth in Red Wine

Ok, so first we need to get some spillage...
In my case, I decided to give the cloth a proper soak for about 3 mins in the red wine.

Step 2: Step 2: Applying Substances to Remove Stain

Ok, so the wine got spilled, what to do?

We give the cloth a good wring out to get rid of excess liquid.

Step 3: Step 3: Apply Salt and Milk

Now we prepare our salt and milk. I took my milk right from the fridge.
To make the application easier, I cut the cloth in two pieces, which we will be able to compare later on.

Step 4: Step 4: Add Our Two Potential Clensers

Now it starts to be interesting:

1) apply salt to one piece of cloth

2) soak the other cloth in a glass of millk (obviously if you has spilled wine over a whole table cloth, you'd rather use the sink or bathtub and about a lier of milk to cover the stain!)

We leave the cloth soaking and coverred in salt for about 60 minutes.

Step 5: Step 5: Remove Remedies From Cloth

After one hour I removed the cloth from the milk, wrung it out and put it int he sink.
Same thing with the slat cloth, I gave that a good rinse in the sink and left it there for comparison...
The darker red one in the top right corner is the slat cloth.
off to step 6....

Step 6: Step 6: Add Castille Soap

Now the last cleansing step:

*) we add some castile soap (this is an olive oil based, environmentally friendly soap I use in my household)
=> interestingly the stains turned into a greenish color once the soap hit the fabric...

Huh...

*) so give it a good scrub with some COLD water and a brush.

I scrubbed both clothes for about 3 minutes under running cold water!!

Step 7: Finale: and the Winner Is....

After rubbing and scrubbing both clothes for 3 minutes it seemed that all the color had been removed.
Since the light in the bathroom is not the best, I gave both cloths a wring and took them out into the sun....
And tadaaaa:

The milk cloth looked like new, no stains to find.
The salt cloth was pretty clean too, but you could still see some stains.

Conclusion:
If you spill red wine on fabric, forget salt, get some milk, soak the fabric in it and then wash it with soap and cold water.
Scrubbing might support the process.
I am also sure, that the longer you soak the fabric in milk, the better the results.

Also keep in mind:
this experiment was made under the circumstances of a fresh, wet stain!

So happy bbq-ing and if someone spills it, just soak it ;O)
Cheers!

Step 8: Trial With Soap Only!

Following "lakkis69" suggestion to try it out with castile soap only, I did.
And it does not work as well as with the milk soaking before hand.
The soap stained the cloth greenish again and after scrubbing and rinsing with cold water as before, the stain still remained.
Conclusion: still, if you spill, soak it in milk for long and then scrub ;O)