Scrums
Scrums are a pretty frequent occassion in a rugby match (particularly at lower levels where handling errors are rife) as the scrum serves as a way to restart play. The scrum involves the forwards (or at least eight people) from both teams coming together and pushing against one another to contest for the ball. When a team is awarded a scrum, they are allowed to 'put' the ball into the scrum, thereby increasing their teams chances of winning the ball though the ball can be won by either side, similar to a tip off in basketball.
For example, lets say someone knocks the ball on. The referee will whistle the knock on and mark the spot of the infraction as well as the team he is awarding the scrum to (the team that DIDN'T knock the ball on). The two packs would then go to the spot of the infringement, crouch and then engage over the referee's mark. Neither side is allowed to push until the ball is put into the 'tunnel' which has formed underneath the two front rows.
The cadence for the scrum engagement is usually "crouch, touch, pause and engage" though this will change slightly depending on the referee. On the call to "touch" the two front rows (barring the hookers of course) must reach out and touch the opposition front row to make sure that the two front rows are neither too far away or too close to engage safely.
A scrum must be bound together with three front row players side by side, no more and no less, where the two packs come together. The second row (locks and flankers) will then bind onto the front row with the eight man fitting up last (usually) between the two locks. The scrum should usually have a 3-4-1 look to it as in the image to the right, barring any irregular binds by the loose forwards.
Lineouts
The lineout is the way in which the ball is restarted after it has been kicked or knocked out of bounds. The lineout is 'awarded' (meaning they get the throw in) to the team that DIDN'T put the ball out of bounds.
Players in the lineout can simply jump for the ball without support or they can help lift other players to try and secure the ball (e.g. two players lifting one player by the legs to increase his jumping height).
If the ball is kicked fully out of bounds from behind the 22 (and was not brought into the 22 by the kicking team) the lineout is taken where the ball went out of play.
If the ball is kicked fully out of bounds from in front of the 22, the lineout is formed from where the kick was taken.
If the ball bounces in bounds before going out, the lineout is taken where the ball went out of bounds.