Getting from the set piece to the breakdown
As a supporting player who is trying to get from the set piece to the breakdown, the key is to run a tight line in support which puts you at 45 degrees to the breakdown when you're around 2m away from it. This position gives you options. You can receive a pass from the breakdown, clean out, or support the player with the ball if they're able to break a tackle.
The action you take will depend on the criteria above, as well as whether the tackle is in front of or behind the advantage line. This determination must happen immediately (as an example; if the defense has good line speed and your team has slow ball from the scrum base, then you should anticipate that the point of contact will be behind the advantage line).
Your supporting line should be as direct as possible so that you arrive quickly and in a good position. It's much much easier to protect the ball if you are the first player to arrive than if you're slow to the ball and need to move a defender.
For more on how to move around the rugby field economically, check out our article from earlier this year titled Flanker running lines from ruck to ruck which has a good analysis of how running flat lines as a supporting player can save you a huge amount of energy and help you hit more rucks than anyone else on your team.