By the time I'm posting, it's too late to make the dog vomit. Everyone should know how - you pour a shot of hydrogen peroxide down their throats - but DO NOT do it now!! It's no good to try even a half hour after they ate whatever awful thing they shouldn't.
So, attempt 2 is to get it to pass through them. Withhold all food. Feed them petroleum jelly, as much as you can. It is inert, will not be digested and (fingers crossed) may lube everything right on through. Just smear it on the roof of the mouth like peanut butter.
Provide lots of thinned broth to encourage drinking.
If/when the string starts to pass, DONT PULL. The other poster was not kidding or exaggerating, now you've heard it from 2 people, you can shred the intestine. Literally shred it. This is fatal.
Do cut it so the dog can't pull at it.
If the dog passes the petroleum jelly (this will be obvious) and not ALL of the string get them to the vet right then.
Pay the emergency after hours fee.
Drive however far you have to.
Borrow a car from a neighbor.
Do what you have to do to get them there.
When they eat something indigestible, there is always a chance of blockage, which is really serious. Surgery or death serious. String is so, so much worse. Because it can unravel and get caught up then as part of it tries to pass, the caught part gets tighter.... and tighter. It will cut off circulation to parts of the intestine, which then quickly die.
So, be ready to get gross and wash through greasy dog poo looking for every string. If they don't pass every last one, rush to the vet.