What is the difference between an "objective" and "the methods" in a lesson plan?

Your objective is your goal. It's where you want to be. Like "get home" would be an objective.

The methods is what you do to achieve your objective. For the get home objective, the methods could be walk, ride a bicycle, drive a car, take the bus, or hitchhike.

Or for teaching, objective is something like "students understand the difference in nouns and verbs".

The methods could be lecture, demonstration, discussion, workbooks, videos, educational games, etcetera."

Find what motivates your dog. Some dogs do anything for food. Some dogs do anything for Toys. Some do anything for a good petting. Some do anything for only one type of food, like cheese, or hotdog. Some only have interest in training for 5 minutes at a time, and others can go for an hour. Figure out what your dog is willing to work for, and then work with her in sessions that are no longer than she can tolerate. How to train your dog properly https://tr.im/kZnns

Sign up for a dog obedience training class. It will not train your dog. It will give you training on how you can train your dog. Most people understand the idea of training, but there is a right and a wrong way to do it, and there is good and bad technique. Timing and consistency is very important, and it helps to have feedback of someone watching you who can help you improve your technique to get more efficient results with your dog.

However, she may be somewhat anxious around other dogs, sort of like the shy kid on the playground. She will benefit from continuing what you are doing as far as asking her to sit before entering, but there are more things along those lines that will help her to calmly go in and out of the dog park. She may also benefit from going in short bursts, or only when fewer dogs are present, or avoiding times when other dogs that make her nervous are present. Maybe she just plays loud - my brother's dog is this way - or maybe she is a dogpark bully - sorry it is possible. But more likely she is just a little anxious around new dogs and she wants to play but just doesn't quite know how to do that and still feel comfortable. Don't be surprised if your dog does not actually like the dog park, and maybe she would get more enjoyment and less stress out of simply going for a good walk somewhere else.

A wagging tail does not mean that your dog is happy or even comfortable with the situation. It means your dog is emotionally aroused. This could be a happy arousal, or it could be a nervous arousal, or it could be an aggressive arousal. Go youtube it, there are plenty of videos of 'vicious' dogs who are throwing a very aggressive fit of barking and snarling while their tail is wagging vigorously. Even police dogs who are not let off the leash to chase down a suspect can be lunging and barking and snarling, and their tails are still going.