Well that "any similar material" bit constantly improved over time and nowadays soccer balls reached near-perfection. Almost each World Cup brought a new type of soccer ball, with improved characteristics, although all of them stayed inside the official soccer rules stated in the Laws.
The goal kick (3) is awarded to the defending team, if the attacking team took the ball out of play on the defending team's goal line. The game is restarted with the goalkeeper kicking it from within the safety box. If the defending team touches the ball last and it goes over their own goal line, outside of the goal itself, then the opposing team earns a corner kick (4) and they will be required to restart the game from the corner nearest to where the ball went out.
An indirect free kick (5) is awarded when a team produces a non-penal foul (dangerous play or offside for example) and the game is restarted with a ground kick that cannot be taken towards goal (if a player scores directly from an indirect free kick, without another player touching the ball, the goal won't stand). A direct free kick (6) is caused by a foul or handball and unlike the indirect free kick it can be struck directly towards the goal.
A penalty kick (7) is similar to a direct free kick in that it is caused by a foul or handball, but the offence occurs inside the defending team's penalty area. The game is restarted with one of the attacking team's players shooting for goal from the penalty spot (11 meters, perpendicularly on goal), with nothing but a goalkeeper to beat.
The last of these eight soccer rules is rarer and it's called the dropped ball (8). The dropped ball occurs when the referee stops the game for a special reason (an injured player, ball becoming defective or the interference of an external factor) and the game is restarted with him dropping the ball from shoulder height in front of two players who will battle for possession (sort of how basketball matches decide initial possession).
One extra soccer rule regarding the goal kick states that the kick must be powerful enough to pass the penalty area. So in case the goalkeeper executes the goal kick and passes the ball to a teammate in his own penalty box, the goal kick is re-taken.
The same rules as for a direct free kick apply, in that opposing players must be at least 9.15 meters away from the corner, the corner taker may score directly from the corner kick and the kicker can't play the ball a second time until it's touched by another player. The only additional rule is that the ball be placed in the corner arc.
Well that's pretty much all you need to know about soccer and soccer rules. Most of these rules seem harder than they actually are on paper and if you watch a couple of matches you'll soon get the hang of them naturally. The only one that requires some special attention is the offside soccer rule, which indeed can be harder to understand without the proper explanation, so check out the offside article on the site for a more detailed clarification on that.