What is the lesson in Jane's rebellion and attempt at freedom? Is there a better way she could have handled her oppression? Do we see this in the world today?

Jane's rebellion takes place within the context of the patriarchal society that oppresses her. The room with the yellow wallpaper is symbolic of her imprisonment within the system set up by her husband, a doctor, and her brother, who is also a doctor. Trapped by the system they have set up for her, which is intended to be coddling but is also infantilizing, she sinks deeper and deeper into depression. Her husband's treatment of her is representative of the male medical establishment of the time, in which women's complaints, which often arose out of boredom (for wealthy women, who also had servants), were treated with a debilitating "rest cure." 
Jane's rebellion consists only of peeling the wallpaper off her walls, which is, of course, not a rebellion at all. To fully resist the patriarchy of the time would have required her to leave the room with the yellow wallpaper. She would have had to escape from the infantilizing care of the men around her and to enter the world, in which she could do what she enjoyed, including writing. 
Many people today would agree that the patriarchy controls women. While women are becoming more outspoken about their oppression, the systems of medicine, politics, business, and other realms are still controlled largely by men. In other words, these systems still ensnare women in a system that many people deem oppressive and unfair. It is only by enabling women to construct their own systems or change these systems that they can escape from the oppression of sexism.