It should be noted for the sake of Snoooopy that the numerical designation for a given formation has evolved from a fairly simple and easily derived nomenclature to something of an art form. The easy to understand formations, like 2-4-4, 3-3-4, 4-3-3, etc. were based on fairly simple concepts of how various players on the field interacted with eacy other. A fullback, for instance, would most always stay closer to his goal than his teammates; a forward (striker, e.g.) would push up to the front of an attack on the opponent’s goal, and the mid-fielders would roam the area in between.
Now, however, based on evolution of the game starting with the Brazilian teams of the 60’s, and especially as accelerated by the ‘total football’ concept of the Dutch national team in the 70’s, it is naive to think of players having rigid roles on the field, much as American football can no longer count on a rigid role for, say, a half-back or tight-end. So a ‘formation’ becomes more of a generalization about organizational philosophy for a team, rather than a strictly established positional scheme.
Thus, for instance, the 3-6-1 you cited might as easily be considered a 3-4-3, or a 3-4-2-1, or a 3-2-4-1, or any other such combination. By calling it 3-6-1, the team is expressing a philosophy that the only player commited to attacking is the one ‘forward’; the six ‘midfielders’ are all committed to some version of connecting the play at the back with the play ‘up top’ (close to the opponent’s goal, which on a diagram is at the top). But if what they have are two really committed defensive midfielders, you could just as easily consider it an aggressive 5-4-1, with two forward fullbacks.
And we won’t even go into the difficulties under the numerical system of properly designating ‘sweepers’ and ‘stoppers’.
The ‘Backpass’ Rule
Correctly stated, this rule prohibits the goalkeeper from handling a ball kicked to him intentionally by a teammate, or thrown to him by a teammate (see Law XII, Laws of Soccer). The infraction results in an indirect free kick from the spot the goalkeeper touches the ball. If a player attempts by subterfuge to pass the ball to a keeper in such a way as to circumvent this rule (for instance, lifting a ball on the ground with his foot into the air so he can head it back, or falling to the ground to ‘knee’ the ball back), the player is penalized by being ‘cautioned’ (yellow card) and the other team gets an indirect free kick from the spot the player attempted his subterfuge. This does not apply to attempts to play the ball to the keeper where the method used results from the natural flow of play (as, say, heading a ball in the air to the keeper).
Soccer 'Plays
This is what we call in soccer ‘tactics’. There are several well-known soccer tactics that you can see occur on the field. Because the play rarely is allowed to start from a standing stop, such tactics are usually not pre-existing designed plays such as you see in American football or even in basketball. It is much more like the simple application of concepts from basketball like screening, pick-and-roll, give-and-go, etc.
Some common soccer tactics you will see include:
- The ‘wall pass’, where a player with the ball who is confronted by an opponent will play a ball laterally to a teammate, who immediately returns a pass to the first player beyond the interposed defender. The first player will have sped past the defender, and the effect is similar to having played the ball off a wall to himself.
- The give-and-go. This is similar to basketball, you probably recognize this sort of play already.
- The crossing pass, where a player on the wing will send a pass across the mouth of the goal, hoping to allow a teammate to re-direct the ball into the goal. English football is filled with such attempts; to watch quality crosses, watch a game by Manchester United with David Beckham on the right wing. Interestingly, England’s national team suffers from the lack of someone to cross from the left, a constant theme of those who are upset with results of the national team.
- The overlapping run, where a teammate of the person with the ball runs from behind the one with the ball to a position forward and wide of him. This type of run allows a pass to the overlapping player, who can continue the run down the wing in possession of the ball, hoping to get behind the defense and either steer towards goal or make a cross. Brazil does this all the time, on both sides, and it is a very effective weapon. Of course, it does leave the team vulnerable in back of the ball, in case the opponent obtains possession and starts a quick counter-attack.
There are endless other such ‘plays’, but they consist of application of specific 1v1, 2v1, 2v2, and 3v2 tactics to generalized strategic goals, as played out in infinite variation on the soccer field. The “beautiful game” the Brazilians call it; I hope you enjoy it. 
(Note: confirmed soccer junkie and ten-year referee, seven-year coach here, griping bitterly that his last move deprived him of Fox Sports)