There are 12 players on each team, 2 goal keepers and 10 field players. There is one goal keeper and a maximum of 6 field players on court at a time. Substitution can occur at anytime so long as player-off before player-on.
The ball-playing rules are in 3's. 3 steps with the ball (a full three steps too, landing after catching the ball is step 0) but no pivoting like basketball.
3 seconds holding the ball.
3 m from the player when they are awarded a free throw. Hence the 9m line. All free throws (not including 7m penalties) from fouls between the 9m line and the 6m line go back to the 9m line. This is because the free thrower gets three meters but the defender gets to stand on the 6m line in order to guard the goal.
Dribbling is allowed (but slows down the ball, passing is better). The ball must be patted down, not carried like in basketball. No double dribble - the sequence of events with the ball can be catch (ball under your control), 3 steps, dribble, catch, 3 steps, - must pass or shoot.
No time waisting. There is no shot clock, but if the refs (there are two) think you havn't been trying to score then you'll lose the ball. Whether after 10seconds or 2 minutes.
If the ball goes out over the side (all the ball passes completely over) then the other side gets it. If the goal keeper directs it over the back line when saving the goal then its still the goal keepers (unlike soccer). If the defenders direct it over the back line in blocking a shot then it goes back to the attacker. If the attacker misses and throws it over the back line then they lose it of course and its a goal throw.
A goal is scored when it passes completely over the back goal line within the goal. Player resumes at the center line with the non-scoring team in control of the ball.
The goal keeper is the only player allowed in the goal area (6m semi-circle). (The goal area includes the line (5cm wide) so you can't contact any part of the 6m line or inside it.) They are also the only player allowed to touch the ball with their feet (below the knees), but only to save a goal, not to direct it out of the goal or to control the ball when it is not being shot at goal.
The attackers may shoot from in the air above the goal area but must shoot before landing. A defender (or an attacker can not travel through the goal area in order to get an advantage at another spot, (no short cuts). Casual entry into the goal area is OK. The rule only applies if you are seen to gain some advantage by entry into the goal area.
The goal keeper can play as a field player, but the transition must by without the ball, ie if the goal keeper comes out in control of the ball - its a 9m foul. If they go in in control of the ball - its a 7m penalty. If you pass the ball back to your own keeper when they are inside then its a 7m too.
Attacking fouls. No bargeing or head ducking (lose the ball).
No using the elbow or palming off.
No swiping away the defenders arms with your hands to get past them.
Basically just don't use your arms (that is if the ref sees you :-)
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The're are a few others, a rule book full, but they are the main things.
The only other one of major interest is how one can gain possesion of the ball and block an attacking player. Handball is basically a non-brutal contact sport, but non-brutal varies with the strength and class of the players. Theoretically one can only use your torso to block the path of any player. If you use your arms to push or grab the player then its a free throw to the attack. However, we don't have free throws at the goal like in basketball. Usually its inside the 6m and you must go back to the 9 and start again, That is you lose your momentum. So the refs allow play to continue if you are still in control of the ball and can play on with out making too many steps or touching down inside 6, or making a bad pass that get intercepted basically because you were hit, ... , in summary, the attacker gets the advantage.
If the defender fouls you while you're making a fairly certain shot at goal then you get a 7m free throw. Thats just you and the keeper, no defenders. plant one foot behind the 7m, wait for the whistle, you've got three seconds. If you lift your planted foot (the forward one) then its not counted. If you slide it onto or over the 7m line then its not counted. If it bounces off the goal posts then its still in play.
The punsishment system : 1 warning (yellow card), 2 2-minute suspensions (2 fingers) (ie second warning is 2 minutes), 1 disqualification (off forever but with replacement after 2 minutes) (red card)(ie third 2 minutes is disqualification), and exclusion (crossed arms)(off forever but without replacement (ie team plays with 1 less player for the rest of the game).
Simple fouls get no punishment - ie checking player with arms when they are in front of you by knocking the ball arm and controlling the body. However the attack gets a free throw if they don't get advantage. A warning is for something like pushing or holding the player while they try to get away or holding from behind. 2 minutes or higher can be given straight away for some more serious fouls, ie brutal push (2minutes), punching or fighting (disqualification) punching ref (exclusion and probably banned for life too).
Generally you only give 3 warnings to a team.
You don't give both advantage and a free throw either. Basically if they get advantage and regain control of body and ball then they're on their own.
Typically a shot at goal from 9m in which the arm gets hit while shooting, and which misses, deserves a free throw. A similarly fouled shot from 6m or closer (ie with no chance of a block from a defender) deserves a 7m penalty. (This situation is good for wing shots which have no angle in first place but get a penalty throw if fouled while jumping in and shooting.)
Free throws (including penalties) and Punishments are sort of orthogonal. Free throws are more about the right to play the ball without interference. The punishments are more to do with brutality and player behavior.
Its pretty hard to explain these things in summary - you have to train hard to be a good ref. It takes awhile to learn what applies when and where because the situations can be quite complex. Its also hard to see how a high level match arises from this summary of the rules. Basically you have to see it. There are probably books in your library.