How does the Ascendant determine the lordship of each house?

Planetary sign-rulerships are fixed — Mars rules Aries and Scorpio, Venus rules Taurus and Libra, Mercury rules Gemini and Virgo, the Moon rules Cancer, the Sun rules Leo, Jupiter rules Sagittarius and Pisces, and Saturn rules Capricorn and Aquarius. Once the Ascendant sign is known, each of the twelve houses is assigned a sign moving forward from it, and the ruler of whichever sign lands in a house becomes that house's lord for that individual chart. This is why the same planet can be the 10th lord for one person and the 6th lord for another — the underlying sign rulerships never change, only how they map onto each person's houses.