Basic rules:
At the start of each game, separate the deck into major and minor arcana. Shuffle the minor arcana and draw 7 cards each from it. Draw a card from the minor arcana to be the starting minor discard card. Shuffle the remaining major and minor arcana together to form the draw pile.
On your turn, you must either play a card from your hand (which will be either a major or minor arcana) or draw one. If you can't play, you must draw, but you must play a minor arcana if you can. The minor arcana function as normal uno cards do. For example, on a 5 of pentacles you may play any other pentacle or any other 5, or the ace (wildcard). The major arcana do special things and can be played on your turn regardless of the last played card. Play into two discard piles split between the minor and major arcana. Whenever you discard cards for whatever reason, put them underneath the correct discard pile so the last played card is unchanged. When the draw pile runs out, shuffle the minor discard to find a new starting card, then shuffle it together with the major discard to form the new discard pile. If somebody starts drawing cards but runs out partway through, they are absolved of drawing more... for now. 
You win by playing a minor arcana when it is the only card in your hand. If your hand is emptied by other means, you must draw a new card immediately. You can also win from the effects of major arcana, but only by emptying your hand if the card specifies 'playing' instead of 'discarding'. When you have just one card left, you must point this out. Say 'taruno' or 'pentacles' or any catchphrase you like.
Special cards:
Kings, queens, knights, and pages function a little differently. The King allows you to set the suit to whatever you like (but must be played on a correct suit as all other cards) skips the next player's turn, and makes the next player draw three cards. It's almost like +4 in UNO, but, y'know, it's 3. The Queen just lets you change the suit. The Knight just skips the next player and makes them draw two cards (+2 card). And The Page reverses the turn order (reverse card). These are called the face cards - they are the only face cards. 
You can stack +3s and +2s, but not on eachother! Just like in the best house rules of UNO, a player affected by a King can play a King (but not a Knight) of their own on top of it instead of drawing, and same goes for a victim of a Knight.
The Ace isn't a face card, but functions as a wildcard (you can play it on anything); however, it only switches the suit (and number) to what's written on the card. Note that the rule about drawing only if you can't play a minor arcana extends to the Ace!
All major arcana have special functions. Good luck.
0 THE FOOL: Any cards people have face-up in front of them are discarded, removing their effects. Shuffle both discard piles into the draw pile. You discard your whole hand, and draw 7 cards. 
I THE MAGICIAN: You put a card up your sleeve. Not literally, though, unless you want the cards to get dirty. Just put a card from your hand face down in front of you. You may return it to your hand at any time, but otherwise it does not count as being part of it. You may not look at it without returning it to your hand.
II THE HIGH PRIESTESS: Look at the top cards of the deck equal to the number of players. Put them back in whatever order you like.
III THE EMPRESS: Discard all non-face cards (including major arcana!) from your hand and draw that many cards. All players must discard all of their own face cards.
IV THE EMPEROR: Discard all non-face cards from your hand. All players must give you all of their own face cards.
V THE HIEROPHANT: Choose a player who has a different number of cards to you. If they have more, they must give you cards until you have equal numbers or you have more. If they have less, you must give them cards until you have equal numbers or you have less. Basically, this evens your hand sizes.
VI THE LOVERS: Choose a player. You two are now a team. If either of you wins, you both win. However, you now must always draw one card at the start of your turn, even if you can play (this makes it very hard for you to be the winning player). You may show your hands to eachother! Yes, it is possible to have everybody win using this card. 
VII THE CHARIOT: Leave this card in front of you. For the rest of the game, after playing a card, you may put it in somebody else's hand instead of the discard pile. Playing a card this way can never change the current suit or number. Everybody except you draws a card. 
VIII STRENGTH: On this turn only, you may keep playing minor arcana without ending your turn until you cannot anymore. Face cards have no effect. You can win from this!
IX THE HERMIT: Leave this card in front of you. Major arcana played by others can no longer affect you. If it's in front of you, place this card in the discard when you play a major arcana.
X THE WHEEL OF FORTUNE: Everybody rotates hands clockwise. 
XI JUSTICE: Players with the most and the least cards swap hands. In case of a tie, you decide who swaps (out of the tied players).
XII THE HANGED MAN: Discard all but one of your cards, but skip your next turn. Leave this card in front of you for now to mark that you're skipping a turn.
XIII DEATH: The first time in a game this card is played, everyone discards one card. The next time, you all discard two. Then three, and so on. If this empties anybody's hand, they win and the game ends immediately. If this causes a tie, the winner of the tie is decided by fate: they each draw a card, and the highest ranked card wins (Major arcana > minor arcana, then by number. Ties in the minor arcana are resolved by Swords > Cups > Wands > Pentacles). 
XIV TEMPERANCE: Discard all your major arcana. Nobody may play major arcana until you next play a card. Leave this card in front of you to mark this.
XV THE DEVIL: Pick up all cards in the major arcana discard pile, not including The Devil.
XVI THE TOWER: Next player skips their turn and draws all of the cards in the draw pile. However, lightning can never strike in the same place twice, so if they've already been affected by this card this game absolutely nothing happens. The only correct way to play this card is by raising it above your head and then dramatically slamming it onto the table.
XVII THE STAR: Leave this card in front of you. When made to draw while it's in front of you, you now only draw half as many cards as you're meant to, rounding up. If it's in front of you, discard this card when anybody plays The Sun, as the sun is a star after all.
XVIII THE MOON: Discard at least two cards from your hand, then draw that many cards.
XIX THE SUN: Everybody discards a card of their choice.
XX JUDGEMENT: Any player of your choice draws twice as many cards as you have in your hand.
XXI THE WORLD: Give one card from your hand to each player. Then everybody draws a card, including you.
ADDENDUM:
What happens if you just run out of cards to draw entirely? Keep playing for as long as possible. If there's just one card left, either use it to play or draw depending on what the current player does. If there are zero cards left on the table and you're asked to draw or have to play a minor arcana, then your quest is over. Resolve the victor with the Death rules.
If you can play a kinght or king to stack, must you? No.
Can you play a major arcana even if you can't resolve its effect? Yes. Do as much of the effect as you can. For example, if you play The Moon with only one other card in hand, just discard and draw that one. If you play The World with less cards than there are players, you choose who misses out.
Why are we playing into two different piles?
The minor arcana you are allowed to play is determined by the last played minor arcana. If you played major arcana into the same pile, it would become difficult to tell.
Does playing this game count as doing a tarot reading? Every card you draw is part of a reading to answer the question of whether or not you will win the game ;)

[Sorry if you can't understand the rules, it makes sense to me. Rev 4.6.2]