They probably don't in the very low end P&S cameras or at least they don't have a lot of flexibility, but when you move up into the compact cameras, you get more features. What you might do is look at the Canon G12. If you look at the features it has and use it as a bases to compare other cameras in that class, you will get an idea of what is available in the fixed lens compact models. I know that price is dependent on one's perspective, but I was surprised at how low the G12 was compared to the G11 and G10. If you read the reviews they also mention the cameras they compare to the G12 and why they are better or the G12 is better. Even if the G12 or one of it's competitor cameras is higher than you want to spend on a camera, just knowing what it's features are will give you a better idea of what to look in the cheaper, but less featured packed cameras.
Photo classes can help, especially if it's focused (no pun intended
) on the specific areas that you are interested in. Some classes are geared towards the masses so you never really get into any depth on a particular area, which is ok for someone that does want a overview of the basics, but usually leaves you with more questions than answers. I've always found that practice, practice, practice, helps... as long as you are able to learn from your mistakes. It's hard to learn if you don't understand why something isn't working and there are times that one class or even a few hours with someone that does know the answers came make all the difference in the world to getting better. But you still need to practice.
Mike