Planetary rulers of the days of the week

"Monday's Child is fair of face,
Tuesday's Child is full of grace,
Wednesday's Child is full of woe,
Thursday's Child has far to go,
Friday's Child is loving and giving,
Saturday's Child works hard for a living,
But the child born on the Sabbath Day,
Is fair and wise and good and gay."

The ancient Babylonians chose to organize their calendar around 7 days of the week, and each day corresponds to one of the seven "planets" visible to the naked eye. [Planets is in quotations because two--the Sun and the Moon--are technically not planets (they're luminaries).

Monday (lundi in French) is ruled by the Moon. "Monday's child is fair of face" might refer to the sensitivity and youthfulness associated with the Moon.
Tuesday (mardi in French)  is ruled by Mars. "Tuesday's child is full of grace" might be more aptly interpreted as full of energy and movement.
Wednesday (mercredi in French) is ruled by Mercury. "Wednesday's child is full of woe" might be interpreted as a person who worries or thinks too much.
Thursday (jeudi in French) is ruled by Jupiter. "Thursday's child has far to go" might thus be interpreted as a person who will travel and learn.
Friday (vendredi in French) is ruled by Venus. "Friday's child is loving and giving" might refer to the Venus nature, that is, a person who is loving and receptive to love.
Saturday (samedi in French) is ruled by Saturn. "Saturday's child works hard for a living" thus might refer to the Saturnine nature which is rather serious and responsible.
Sunday (dimanche in French) is ruled by the Sun. "But the child born on the Sabbath Day is fair and wise and good and gay" might refer to the magnanimous Sun nature.
Astrologers generally pay more attention to the ruling planets in a natal chart. That is, the planet that rules the sign on your Ascendant and the planet that rules the sign of your Sun. For example, if your Ascendant is Aries, Mars is the ruling planet of your Ascendant since Mars is the natural ruler of Aries. If your Sun is in Taurus, then Venus is your Sun's ruling planet since Venus is the natural ruler of Taurus.

Each of the 12 signs in the zodiac falls under Fire, Earth, Air or Water. There are three of each.
The fire signs are: Aries, Leo and Sagittarius
The earth signs are: Taurus, Virgo and Capricorn
The air signs are: Gemini, Libra and Aquarius
The water signs are: Cancer, Scorpio and Pisces