Here are some tips for beginners:

Just go out.
When you play mahjong for the first time, forget about going out with lots of combinations or points - just worry about going out properly and getting used to all of the basic rules.

Stick to the basics.
Once you get going out down, it's time to go out with lots of points and awesome combinations. But there are so many combinations; which one(s) should you collect? To keep yourself from becoming overwhelmed, just focus on the basic combinations. Only worry about the advanced combinations after you have a good grasp of the basic combinations.

Improve your hand.
When you are one piece away from going out, instead of just waiting for the one piece to go out, try to improve your hand. For example, if you have tiles 1-8, try to get rid of the 1 so you have an inner numbers hand (2-8). Or if you have a 1,2,3 and 2,3,4, try to collect an identical straight of 1,2,3 & 1,2,3 or 2,3,4 & 2,3,4. And so on. Of course, if the winning piece comes out, don't hesitate to go out, but while you are waiting, improve your hand.

Work with what you have.
Just because you're losing, don't push your luck by trying to go for a huge hand. Try to go out with the hand that you are closest to completing. Remember that as long as you go out, the game is still alive.

VI. Freestyle Play

(Another rule I've made up)
In order to make the game interesting, I have come up with the idea of freestyle play. What I mean by freestyle play is playing mahjong according to the rules of the current dealer (the one who rolled the dice). Don't worry about these until you've mastered the basics or you'll just get overwhelmed with information

Wild card: The revealed tile in the center is a wild card during the dealer's round.
Minimum point rule: No player can go out unless his/her hand has at least 1 point.
Dealer's continuation: If the dealer wins, s/he continues as the dealer.
Steal points from others!: If you go out by stealing from someone else, the points you earn are deducted from the player you stole from. If the player has insufficient points, the stealing player earns an extra round as dealer or another bonus tile for each unaccounted point.
Prevent losing!: When an opposing player reaches 10 points, you can keep the game going by giving up enough of your point(s) to drop your opponent's total points to 9. This is good if you want to keep the game going longer.
Reveal bonus tiles with a steal: Whenever a steal is made, a bonus tile is revealed. A maximum of 4 bonus tiles can be revealed each round. The dealer decides what type(s) of steals reveal a bonus tile.
Bonus tile madness!: The round starts with 4 bonus tiles revealed.
Gambling: During one of your turns, you can place any number of your points into a pool. If you or your team member goes out, those points will double. However, if one of your opponent's goes out, s/he will gain those points placed into the pool. Furthermore, a gamble cannot be made on the same round you go out.
Punishment: If you go out with a hand that is not valid (i.e. violates the dealer's rules), all of your points will placed into the pool.
Team play: A team cannot win unless each team player has gone out at least once.
No stealing: No stealing is allowed during the round except when going out.
Traditional rules: Very tough, restrictive rules. This is how real mahjong games go. I don't like it cuz it's too restricitve and low-scoring.
Make up your own!: As long as it applies to everyone or takes affect at random through a dice roll, make up any rule(s) you'd like. Be creative!

VII. Traditional Rules

For those of you who are interested, here are the the traditional rules.
* All players start with 25,000 points. Stealing points system.
* Dealer gets 1.5 more points. Self-pick takes points from everyone.
* 1 point minimum to go out. Bonus points do not count as a minimum point.
* All straights combination must be non-stolen. The last piece required must be a ryou-men-machi (i.e. 4,5, waiting for 3 or 6; 7, 8, waiting for 6 or 9).
* Identical straight combination must be non-stolen.
* Closing your hand allowed for any non-stolen hand. Hidden bonus tile applies only to closed hands.
* Only a 4-of-a-kind reveals an extra bonus tile.
* 3-of-a-kind for a wind tile only counts if it is your wind or the wind of the round.
* 3-of-a-kind steal can be done from any player. A steal for a straight can only be done from the person right before you.

Alternate rules: one 5 tile of each suit is a bonus tile, random player gets double points if s/he goes out, no stolen inner numbers hand allowed, no hidden bonus tiles, game ends when someone goes negative, lose points if you don't go out at least once.

Log, 2002.7.13
A 10-9 team game lasted 1 hr 30 min, with each round lasting about 10 minutes. Rules were:
* 1 point minimum steal from anywhere
* a 3-of-a-kind for any wind tiles is 1 point
* bonus tiles: 5 revealed, bonus points that can be cashed are dependent on difficulty of hand
all hands can be stolen

Additional rules I'm thinking about adding:
- a non-stolen hand reveals a hidden bonus tile for every revealed bonus tile
Round starts with 1 bonus tile revealed, every steal reveals another bonus tile. Maximum of 7 bonus tiles can be revealed.
All players start with 10 points, play 8 rounds. Someone goes to negative points, game is over. Steal points from others. Problem: how to assign self-pick points for dealer.
Lose 1 point for fake going out.

If you've understood what I've explained so far, you're now ready to begin playing.  There are still some more details such as combinations that are similar to what a pair and royal flush is in poker, but since it can become overwhelming for beginners, I don't think you need to worry about that until you actually start playing.  I'll show those to you after you've mastered the above rules or unless you insist on seeing them right now.