The Japanese Emperors are known to be powerless and been that way longer than they had one and the shoguns are the true powers of the country throughout most of there history..but how would a similar ambitious Ruler with similar circumstances as the Emperor above rise there political power and make there title be known as the country that runs it rather than your ancestors family founding it and ruled it before?
I think this is where fascism could help (the emperor, not the people). This is similar to exactly what happened to Japan before the world war. The emperor has to tell the people that the dignity of the country and the self-respect of the people are both directly related to the wishes of the crown. Because at the end of the day, that is what a monarch is, right?
All you need is to make a political party (assuming democracy) or another institution that relies on the monarch. Once the monarch gains enough power, a starwars type "crisis" could do the trick. In a war, the monarch can get emergency powers that could also give him enough power over the army. Then it is just a matter of time before the monarch could put loyal people in key positions to overthrow the previous government and gain power.
For an ordinary person, all the steps are very hard, but for a monarch that has cultural influence over the people and is the symbol of national identity, this might be easier (not saying that it would be easy though).
PS: I had love to discuss this case even further in the comments…………
By recruiting an army and taking control.
This nearly happened in Japan, a sect of warlike monks were attacking another sect and the emperors guard suppressed the fighting and then he recruited these armed monks to fight for him.
Anyone like a Shogun will have powerful and ambitious enemies. The Emperor got a few of these on his side, won some battles even but was outmaneuvered before his forces could link up. If he'd been more competent or the Shogun less, it may well have happened.