Raising your first House takes a year and a day and costs you nothing. The next House you raise costs 1 point of power. Raising a House in a realm where you have one or more other Houses costs double the previous amount you spent. If you spent 1 point, then it costs 2. If you spent 10 points, then it costs 20. If you raise a House in a realm where you have no other Houses, it costs 1 more than the previous House. If the previous House cost 2, it will cost 3, if the previous House cost 10, it will cost 11.
Your House generates power which you can use within its confines. The calculation for generating House power is 10 x the number of initiations you have, plus 2 times the cost of those initiations. House power regenerates at a rate of 5 per day.
You can devote a proportion of House power to its defenses, how well concealed it is. You can also use it to generate expendable power. The cost to generate expendable power is 1 point for every 1 point of expendable power per year. The cost to generate essences is 1 point for every 10 essences per year.