Since this question spans a long time, I'm sure there were changes in the paths to power open to women. The era I'm most interested in would be the Tang and Song dynasty and the chaos in the time between them. But a general overview (if possible) would also be appreciated.
I guess that women from powerful families had a better shot at power than those from lower classes, so if that guess is correct, assume that I'm asking about women from the nobility.
The Tang dynasty you are interested in happens to be host to Wu Zetian, empress dowager and later empress regnant. She was one of the most influential rulers in China's very long history, being the one who first instituted the system of national exams which promoted and employed government officials on the basis of merit.
As for how she rose to power, she was the Emperor's concubine, who later married the Emperor's son, and then took control after the Emperor had a debilitating stroke. More generally, the concubines in ancient China were considered to be very powerful, having direct access to the ear of the ruler. Sending one's daughter to the Emperor's harem was considered the highest achievement for her and the family, and it was highly sought after by nobles and plebeians alike, as siblings and family members of concubines were often promoted to high positions (two of the Han dynasty's greatest generals, Wei Qing and Huo Qubing were both related to the concubine-turned-empress, Wei Zifu).
As an aside, the drama and hidden battles within the Emperor's inner court has captured in imaginations of modern fiction writers in many Sino-influenced regions. They are a popular subject for prime time soap operas in China, Taiwan, Hong-Kong, and South Korea have similar dramas set in their own courts which follow very similar formats.