The 22 Major Arcana can be assigned to the planets and zodiac signs in astrology. The earlier discussions in AstroTarot Essentials show which of the 22 Tarot Spirits is matched with which planet and sign.

The decans represent divisions of the familiar zodiac signs into three 10-degree segments for each sign, or 36 discrete decans. These divisions are also called the faces and each one has one of the traditional planets as its ruler or decan lord. The Picatrix also includes images for each face. There are three different systems for assigning the decan lords to the decans (all available at astro.com): 

• Chaldean decans, starting with Mars in the first decan of Aries and then progressing in Chaldean (Babylonian) order through the seven visible planets - the most common approach and the one used in the Picatrix for faces.
• Manilius decans use signs rather than planets as the decan representatives.
• Traditional decans (including the outer planets)

The pip tarot cards from 2 through 10 are each assigned to one of the decans. The diagrams below show the assignment. The suit elements (wands=fire, pentacles=earth, swords=air, and cups=water) are matched to the zodiac sign elements. The outer ring of the left hand picture below shows the tarot card suit symbols and numbers that are assigned to each decan. The planetary decan rulers are shown in the third ring from the outside.

In most early tarot decks, the numbered cards had spots (pips) or symbols that matched the number of the card. For example, the six of cups would have 6 cups on it, just like there are 6 hearts on a modern playing card for the 6 of hearts.

General thought is that the first deck with pictoral scenes on the pip cards was the Waite-Smith deck, created in 1909. In fact a much earlier deck, the Sola-Busca deck claims that distinction. 

You can either start with a pip (numbered) card from a reading or with a planet in your chart.

Start with a pip card. Decans or faces are assigned to all the pip cards numbered 2 through 10. On the left hand picture below, look for the suit symbol and card number in the outer ring. On the right hand picture below look for the names of the suits and the card numbers going around in a middle ring. When you find the match of suit and number you are looking for, you have located which zodiac sign and decan represents that card. The decans are just 10 degree divisions of the 30 degrees in each sign, moving counter-clockwise.

Start with a planet. Lets say you want to find the decan lord of a planet in your chart. Note the zodiac sign for the planet, and which of the three 10-degree ranges of the sign it is in. That tells you which decan the planet is in. For each decan, you can find its decan lord and which pip card it works with.

Find the decan lord. Look at the (about) middle ring of the circles below with a planet symbol for each decan. That planet is the lord of that decan.

Example. Say your planet Mars is at 18 degrees 57 minutes of Aires. That is the second decan of Aires. The decan lord is the Sun. The pip is the three of wands.

For the two diagrams below, the content of the rings is listed here from inside to outside.

Left diagram:

1. Zodiac sign information: a) symbol for the element, b) modality, c) sign symbol and name
2. Planet symbol for the decan lord
3. Birthday range for natal sun decan location
4. Symbol and number for pip card assigned to the decan
5. Starting sign degree for each decan, moving counter-clockwise

Right diagram:

1.  Zodiac sign polarity: positive or negative
2. Symbol for the sign
3. Sign element
4. Sign modality
5. Suit for pip card assigned to the decans of the sign
6. Number of pip card assigned to each decan
7. Planet symbol for the decan lord
8. Birthday range for natal sun decan location
9. Zodiac sign symbol and name
10. Sign ruler(s)
11. Planet exalted in each sign
12. The court card (K, Q, J) associated with sets of three decans
13. The Princess (Page) and Ace associated signs and decans