Rugby games always begin with a kickoff. The captains of each team compete in a coin toss with the referee to decide who kicks off and who recieves.
Kickoff
The team kicking the ball lines up along the halfway line. The kicker must kick the ball a minimum of 10 meters forward.
The recieving team sets up in a recieving formation, and retrieves the ball off the kickoff to go on offense.
If the ball is kicked into the end zone, the recieving team gets to play the ball from the 22 meter line.
The kickoff occurs at the beginning of each half of the game, as well as after a try is scored.
Stoppages In Play:
After a penalty, the referee can signal to the defense "back 10 meters". The defense
must retreat 10 meters back from where the ball is, and the offensive team can perform a "tap and go".
A "tap and go" allows the offensive team can get set up, and then the player with the ball touches it to their
foot to continue their attack on offense.
After a player has a knock on or makes a forward pass, the whistle blows and a scrum is awarded to the opposing team.
When the ball goes out at the sideline or a player steps out of bounds, a lineout is awarded to the defending team.
Watch this Sevens game between New Zealand and USA to help understand the flow of a typical game. Notice the continuous play and sequence of events (tackles, kicks, passing, set pieces, etc.), and how a typical game unfolds.