Like in baseball, the game lasts for 9 innings; in the event of a tie, extra innings are played.
There are two teams, with three players on each.  Teams with more than 3 players can make substitutions, but there is no re-entering a game. (This can be changed, but players must play a full inning if so.)
You will need at least 1 BASEketball (although an assortment is nice), a playing area (preferably a basketball court or driveway), and at least 6 players.  Scoreboard, shot markers, and props are optional, but encouraged. (Pics of my setup coming soon.)
For the team on offense, after the order of players is determined, a player chooses a square. The squares next to the basket are bunts, from the free throw line are singles, from the top of the key is a double, a bit behind the three point line is a triple, and "behind the meatballs" is a home run. (I've found that the homerun distance can be arbitrary; basically any distance that allows players to make a homerun, but not easily.  Really, all the distances are arbitrary, my specific distances coming soon.)
Any players on base advance the corresponding number of bases, so if a player is on second and a player hits a single, the runner on second advances to third.  Obviously any player making a shot advances to the corresponding base.
The two closest squares on either side of the basket are bunts. They don't put any runners on base, but advance any runners ahead one base and count as an out whether the shot is made or missed. (Cannot be shot with 2 outs.)
If a player misses any shot, it's counts as an out. The player does not have to dribble the ball or run with it, they can just stand there and shoot, but they cannot step out of the square. If they do, it's an automatic out. (or a reshoot, you decide.)  Double plays are possible; see the defense section.
After successfully making a shot you must run the bases, stopping accordingly. If you come up to bat again while on base, another teammate can fill in your spot. If the bases are loaded, a ghost runner can be placed on a base of the offensive team's choosing. (I recommend a player always be at second base if possible, to aid in a conversion.)
"You can't shoot from the same place twice." If any bunt, single, double, or triple is attempted, the corresponding square cannot be shot from again for the rest of that team's inning. To prevent confusion, it helps to mark off the squares that have been shot from; pot holders, bean bags, or CDs work well. (I used old AOL free trial CDs, I had more than enough.) The home run square can be shot from as often as desired.
If a player shoots a single for example, the next player must shoot a shot other than a single; the same applies for all shots.  This prevents constant homeruns or even simple shots like singles. Also, a player cannot shoot the same shot on consecutive at-bats.  If they shot a homerun on their first at-bat, they must choose another shot their second at-bat.  A home run would be an eligible shot on their third at-bat.  This does not carry over from inning to inning.  (This rule is open to interpretation; I interpreted "you can't shoot from the same place twice" three ways.  The first is obvious and, as explained above, means you cannot shoot from the same square more than once in an inning.  The other two ways I interpreted the rule involve not only teams but players being disallowed from shooting the same type of shot in two consecutive at-bats. If you wish to wave this rule for increased scoring, feel free.)
Since it would be too easy to just wait until the defensive team's psyche-out is over, a shot clock is useful to force the player to shoot within a time frame.  This starts when the player steps into the shooting square and is given the ball by the defense or a referree.  A shot clock gives the defense a fair chance at a legit psyche out. (I recommend +-8 seconds.)
After three outs, the teams change sides.
For the team on defense, three players are on the court. Their main defense is the psyche-out, a diversionary tactic to break the shooter's concentration and make them miss.
Typically, two of the players camp out near the basket in order to turn double plays.
The other player stands in front of the shooter, attempting to psyche-out the offense once the shot clock begins. (If there is no double play in order, multiple defensive players can involve themselves in the psyche-out.)  Direct or indirect physical contact is forbidden, but anything else is fair game. Yes, anything; this is the time to be creative and use props.  If contact is made, a reshoot will take place unless the shot is made.  (Any miss is an out, but I only record airballs as psyche-outs, or shots that were obviously missed due to the defense.  Otherwise every miss would be a psyche-out, which takes away from the nature of it.)
Double plays - When the player shoots the ball and misses, the ball is still in play (unless the miss is an airball). This opens up the possibility of a double play (if less than two outs).  Each of the two defenders near the basket have a chance to tip the ball in.  The defender designated to psyche-out is ineligible for a double play attempt. 
If either of the two defenders successfully tip the ball in the basket, the double play is completed and two outs are recorded. In order for the tip-in to be valid, both of the players feet must be off the ground at the time of contact with the ball.  (If one defender has a bad angle, he can tip the ball to his teammate for a chance at the double play.)  Completing a double play results in a runner on base being removed; priority at first base, then second, then third. (I don't bother removing a runner; it doesn't make sense from a technical standpoint but adds to the game.)
Conversions - If each defender misses, a conversion attempt opens up for the offense. In order for this to be successful, the offense must tip-in the ball in the same fashion.  Only a player on base and the shooter can attempt this; after the two defensive attempts the offense gets two attempts. (The second shot is reserved for the shooter.) Once again, they must be in the air when they try, and they only have two chances, one for each player.  If no member of the offense is on base at the time, only the shooter can attempt the conversion (getting one shot).  (If two players are on base, only one can attempt the conversion along with the shooter.)
If either of the offensive players tip-in the ball, the original shot is deemed successful.  If the ball touches the house or another structure, ground, or any player catches it and doesn't release it before landing on the ground, it is a dead ball and no double play or conversion is recorded. (When the offense has their shot at the conversion, my rule makes the player on base (if applicable) be the first one to attempt. The shooter would be the second and final player to have a shot at the tip-in. The shooter cannot be the first to attempt.)

I encourage any of you who actually play to play loosely at first; see which rules work and which ones don't and adapt as you go along.  By the end of a few games you will have a solid set of rules to go by, which will make things much smoother.  Even so, there still might be situations where the rules are unclear, and new rules can be added.