Dan,
Welcome to LabVIEW.
When converting from a text-based language to LabVIEW, the key concept is that LV is based on a data flow paradigm while languages like C are control flow languages. This means that in LV any node (function, VI, etc.) cna execute whenever all the wires leading to it have valid data. The order of appearance of the items on the blocka diagram has nothing to dowith the execution order.
The tutorials are very useful for newcomers.
Now, to your blinking LEDs. One way to do this is to make an array of your LEDs. Create a while loop with a shift register. Initialize the loop with the 10000000 array. On each iteration of the loop replace the subset of the array containing 10 with a 01. Put a delay (Wait(milliseconds) function) inside the loop to control your blink rate. Add a Stop button to exit the loop when you are done with the blinking.
This will be a nice little exercise that helps you learn many of the basic elelments of LV.
Lynn