I'm sure it might be easy for most on here to run out, but I'm struggling to visualize how the run will play out. Just last night I started imagining big pizza slice shapes behind each object ball with the tip of the slice on the object ball pointing to the pocket. These pizza slices are my cue ball landing zones that I want to hop between.
In Phillip Chapelle's book, he essentially breaks a run-out into three steps. A) get control of the table, B) the middle of the run, C) sinking the 8-ball.
The analysis starts at the end (8-ball) and works its way backwards (step C). Where is the 8-ball, what ball of mine can I use to get position on the 8-ball (the key-ball), and what ball of mine can I use to get position on the key ball (the key-ball to key-ball or the lead ball).
Since there are so many orders that run-outs can be made, if you tried to calculate all of them your head would explode. So, from locking down order that leads to the 8-ball, we turn our attention to getting control over the table (step A). You basically have 2 shots to get control over the table, making a couple of balls and then having precise position that one can actually pull off the run-out. Make a first ball and have better position on ANY second ball, then make the second ball and have really good position on the third. At this point you have control over the table and step A is done.
Don't bog yourself down at the beginning (analysis phase) on an overly precise order of things. Subtle errors in position may require your planned order to change, be ready to adapt and follow what you have done to yourself. But do not alter your plan on the key ball or the lead ball, unless the table has changed enough that you can pick a different key ball or lead ball that still leads to a successful runout.
Many ball positions have multiple runout orders, and some positions may have only one, a few, or even none. Learn to spot these positions and duck before you have removed useful interference from your opponent (ball that interfere with your opponents runout but not your runout are useful to you).
In a perfect 8-ball safety, you place your opponent in a position where his only shot improves your position (i.e. removes one or more of his interfering balls from you position). If you can do this so that he has to improve your position and he still cannot sink a ball, you have effectively obtained 3 shots in a row. This is actually better than the opponent picking up the ball and giving you BIH many times.
So for making a 3-ball run, start at the last ball you wnat to pot, and then see which of the other two balls makes for easier to obtain position on the last ball. Then shoot the other ball first.
As to your pizza pie slices, once you get better, you will want to avoid a lot of the dead-nuts straight in shots as these are harder to get position on the next shot. Cuts up to 45 degrees should becomes essentialy dead easy. The larger angles makes it a lot easier to move the CB around the table with less velocity and/or spin.