How do I teach my dog to share toys with other dogs?

I would start correcting the behavior right away, and slowly start working with her to get her into a "Sharing" mood. I am under the opinion that you "share" the toys with her yourself, to play with her and so forth..so I feel that is a good start and build off of that. I would recommend doing your normal play sessions with her, but slowly incorporate the other dog into the play sessions. Within a few months, it should become easy for you to start training her to "share" directly just with the other dog, and if she enjoys playing together with you both, there is a chance she will just start adopting that behavior automatically without any need for real "training".

To practice, fill your pockets with dog treats and be ready to dole them out any time another dog gets close to something your less-than-gracious dog considers his. For example, give your dog a steady stream of high-value goodies and lots of praise when another dog checks out your dog’s bed. If another dog sticks his head in your dog’s toy basket, be ready to reward your dog with a handful of something yummy and lots of encouragement. If you’re playing fetch and the other dog manages to grab the ball before your selfish pup has a chance, let him know that sharing his ball means getting an “atta boy!” and a piece of cheese. Timing is important in order for your dog to make the connection between the other dog interacting with his stuff and the good things he’s getting as a result. If you’re consistent, your dog will become a gracious and accommodating host to his furry sibs and friends. Teaching a dog to share with other dogs doesn’t mean that he always has to relinquish his goods, but it does means that he should be comfortable when pooches are around his “stuff” whether dog toys, bones, food bowls or bed. Keep in mind that a little resource possessiveness between appropriate dogs is usually okay. If your dog already exhibits guarding behaviors, like freezing over the resource, increasing the rate of consumption of it, growling, snapping or chasing others away when they get too close, seek help from a qualified positive reinforcement trainer.

Always swap the dog's item for something else. If you need to take something from your dog, swap it for something else that your dog considers to be equally or even more valuable. You could drop several treats on the ground near your dog, so they have to leave the item to go and eat them. Then you can calmly pick up the item while they’re enjoying themselves. You can teach your dog to drop and swap during fun training sessions. When your dog is playing with a toy, get something they like even better. Offer this to your dog a little distance away from what they already have. Your dog should be enticed to drop what they have and come to get the new item. You can then pick up the original item. Where you can during training sessions, return your dog’s first item to them soon after you have swapped it. This will help them to learn that letting go of something they love can be a positive experience.