Jasmine loved her brother. She would always run up to him and hug him. "You are the best brother ever." She would say and smile at him.
Each of those sentences were individual thoughts. The easiest way to explain it in simple terms is to tell you to do this: When you read the post out loud slowly and calmly, where ever you stop to take a breath should be a period. IF it makes sense to put a period there. Try that first, and then try to step up to the more complex sentence patterns.
Something else you may want to watch for is not using sentence fragments either. It's alright to use small sentences, but if your explaining something then the explanation and the statement itself will go into the same sentence. So, for example...
I held myself in, not allowing any flames to touch another, for fear of causing harm.
In this case, instead of periods you'd use commas. A simple rule is "If it begins in 'if, and, but, or because' then keep it in the same sentence.
Another example would be: "Bonbon loved her sister. Cause to her she was the most wonderful horse in the world."
This is in a couple fragments, and is actually a pretty common mistake. I've made it a few times myself. "Bonbon loved her sister, because to her she was the most wonderful horse in the world."
See? The statement and the explanation are in the same sentence.