You're right that both the in-manual and in-game introductions to Caravan are not very effective. This is what I figured out via a combination of trial-and-error and the instructions.
(Also, I keep the Caravan rules card from the deck that comes with the special edition out when I play New Vegas. Very handy quick-ref for the face cards once you get used to the rest.)
2 players play the game. You can use any cards you want, as long as (a) you have at least 30 cards in your deck and (b) no two identical cards (EG, 2 of clubs) come from the same casino. (In real life, if you wanted to play, they couldn't be the same deck/brand. Unless you frequent casinos enough to have a collection. :)
The game combines elements of blackjack, war, double-solitaire (that is, two player head-to-head solitaire) and even Uno.
Each player is initially dealt 8 cards. Your first three plays to the board must set up your initial caravans -- you have three to set up. Give them each a numbered (ace through 10) card.
Each of those caravans has a suit and a direction. The suit is the suit of the last numbered card dropped on the pile. The direction is either up or down from your starting point. An important thing to note (and I had to lose about a dozen hands before I learned this) is that the direction does not have to be sequential -- you do not, for example, have to follow a 10 with a 9, or a 5 with a 6. You can have the following sequence (which adds to 26): 10, 9, 7.
To play a numbered card on one of your caravans, it must either be going in the appropriate direction, or it must be of the same suit as the last numbered card. However, under no circumstances can you play the same number twice in a row, no matter what suit they are.
You're targeting a range of between 21 and 26 (inclusive) for each your three piles.
During the first three moves, when setting up your caravans, you do not draw replacement cards for those you lay out. Thus, when those turns are complete, you will have five cards in your hand.
Players take turns playing one card each. If you cannot or do not wish to play, you can discard a card from your hand. In any event, once a card is played or discarded, you draw a replacement from your deck. If desired, instead of playing or discarding a card, you can discard an entire caravan.
Play continues until "End game," below.
Cards and Their Effects
- Ace: Always a value of 1. Consider a number card except when a Joker is involved.
- 2 - 10: Face value.
- Jack: Removes the target card and all face cards attached to it from the board. Typically played offensively against the other player.
- Queen: Reverses the direction of the caravan. Can be used offensively and defensively.
- Offensive example: reversing a descending caravan to ascending when the opponent is near enough the target (and at a high enough last number) that the direction switch prevents him from landing within the range. Rare, but very effective when you can pull it off.
- Defensive example: You've been ascending or descending and either can't go farther (at a ten or an ace), or you need to reverse direction in order to land in the target range.
- King: Doubles the value of the target card. Again, can be used both offensively and defensively.
- Offensive example: Double the value of a high-value card in your opponent's caravan when he's at the high end of the target range. Boom, now he's overloaded.
- Defensive example: Double your own card (typically effective early-game) to get a leg up on the competition.
- Joker: This one has different impacts depending on the card you play it against. Often ends up doing "collateral" damage -- that is, damage to you as well as your opponent. Use them wisely.
- Against an ace, removes all non-face cards of the same suit as the ace from the table, except the ace on which it's played.
- Against numbered cards, removes all cards of that value from the table, except the card against which it's played.
The game is over when all three Caravans are successfully sold. When a caravan is between 21 and 26 (inclusive), it is considered sold. However, you can continue to pile weight on a sold caravan, and your opponent can continue to outbid you. Whichever player has the highest bid (without going over) on two out of the three Caravans wins. Ultimately, the goal is to get two out of three caravans as high as possible (preferably 26) before the opponent does, and to prevent the opponent from outbidding you by using offensive maneuvers against him.
But wait -- there's more
In case this wasn't quite clear/useful enough, there's an excellent explanation (with pretty pictures) here.