The only thing I am asking is "how do I know what the ruler of the hour is".
Excellent.
There are three different methods; hard, easy, so easy it's stupid.
The hard method is that you'd have to take the times of local sunrise and sunset, figure out how many minutes is between those two events and divide by 12. Each 1/12 section of that time is a planetary hour. You would do the same thing with that sunset and the subsequent sunrise to get the nighttime hours. This is hard, requires math, and requires knowledge of local sunrise/set times for various locations on the earth. Annoying.
The so easy its stupid method is where you get an astrological program to tell you what the hour lord is. Most display it somewhere, but probably only in classical settings.
The easy method, which is the one I encourage most everyone to use (especially since astro.com does not display hour lords) involves the Sun's position in Placidius charts. By taking a chart and casting it into Placidius, we can determine the planetary hour by counting the half-houses the Sun has moved through.
Here is an example of this moment from my location:
We already see that my program is saying it's the hour of Mars (the super easy way
), but we'll ignore that for now.
So, we see the Sun is located down in the fourth house. We start from the Ascendant and count half-houses in a clockwise motion (following diurnal motion), so from the Ascendant to the twelfth house to the eleventh, etc. So, from the Ascendant to the cusp of the twelfth house is 2 hours. From the cusp of the twelfth to the eleventh is another 2 hours, and so on and so forth until we get to the cusp of the fifth house. The Sun's position on the cusp of the fifth house (exactly!) marks the beginning of the 17th planetary hour of Monday.
Note here that beginning with the Ascendant starts us with 1 hour, so the twelfth house cusp is actually the beginning of the third hour, the eleventh cusp is the beginning of the fifth hour, etc.
Now we have to figure out which half of the fourth house the Sun is in. Is it's position closer to 14° Capricorn (cusp of the fourth)? Or is it closer to 16° Aquarius (cusp of the fifth)? The Sun at 29° is 15° away from 14° Capricorn and 17° away from 16° Aquarius. So, since the Sun has crossed a half-house marker, it's the 18th planetary hour on Monday.
With this in mind, you just have to identify the hour lord. The first step is to identify the ruler of the day, this is a chart for Monday (remember, planetary days begin at sunrise, not midnight), so the ruler of the day is the Moon. The ruler of the day gets the first hour of that day, and the hours go in this order: Saturn --> Jupiter --> Mars --> Sun --> Venus --> Mercury --> Moon --> Saturn.
So, we start from the Moon and go down this order 18 places to arrive at the correct hour lord: 1) Moon 2) Saturn 3) Jupiter 4) Mars 5) Sun 6) Venus 7) Mercury 8) Moon 9) Saturn 10) Jupiter 11) Mars 12) Sun 13) Venus 14) Mercury 15) Moon 16) Saturn 17) Jupiter 18) Mars.
And that's that.
This also works in Regio houses, but it isn't as accurate, so your hours could be off by a bit if you're using Regio. Not really a problem unless the sun is close to a cusp or close to half way.