The truth is she still is a baby to us - but technically, she's a toddler, equipped with her own personality, sense of humor, sensitivities, likes and dislikes. With all these things come emotions. The difficulty at this age is helping him or her to understand what those emotions are and how to deal with them correctly. Right now Sienna deals with frustration, anger and fear in the same way - she cries. There may be some slight variation in the level, sound and severity of the cry, but let's face it, it's a tantrum all the same.
I don't think it's too early to start talking to a 15-month-old about his or her feelings let alone how to deal with them. In fact, I don't think adults give toddlers enough credit in the communication and comprehension area. For example, recently we were going out to see a show and Sienna's grandparents were sitting for the night. I could tell a few minutes before we left that she was getting anxious. What my husband did next was genius. He took a few minutes with her alone and explained to her exactly what was going on. He said that mommy and daddy were going out for a few hours but there was no reason to be scared or frightened because her grandparents were going to take good care of her while we were gone. He also explained that when she woke up in the morning, we would be right there and all three of us would have pancakes together.
Realistically, do I think she understood every word of what he was saying? No, but I think she had a pretty good idea of what was going on. Instead of trying to make the exit abrupt and let her "cry it out", she had a better understanding of what was going on and how to make herself feel better. If nothing else, she was willing to put her fears aside for the sake of a good pancake breakfast the next morning.
The same rules apply when say, it's time to put the toys away. She may throw a temper tantrum but instead of just reprimanding her, it's important to tell her what she is feeling; anger and frustration. Eventually if she can identify those feelings, she'll be better equipped to handle them in the appropriate way when she gets a little bit older.
Below is a website that will help you guide your toddler through different emotions and find appropriate means of self-expression.