Well [@Louis Dabout], you could try to openly assault the throne holding. But that will have your forces counter-attacked by its defenders and those whom would not want your house on the throne.

You could try to marry into the family whom are destined for the throne. Make sure your house inherits the right for the throne. But others will try this as well, and you might want the throne for yourself, not your whiny not even born yet kid.

You could try to secure a majority vote in the council, but there will be others with similar motives, and how do you denounce or assassinate the other council members without getting caught?

There are many ways to fight for the throne. All filled with dangers, how will you approach this? Perhaps you might even be content with supporting another king/queen in exchange for monetary wealth, influence, or both?
How do we fight for the throne? The answer is the almost same, how will you fight for the throne?