For me, the first important idea to understand is that the ladder logic uses 0/1 on off bits to represent input switches, outputs, timer expirations, etc., as well as local states.
The second idea to grasp is that any output controlling bits become active only at the end of each scan by the PLC's CPU. So the order these outputs are turned on within a scan don't matter as long as the logic is correct.
For the machine I'm working on, I identified that there are 5 consecutive states the machine can be in, and I defined 5 bits for these states. With proper programming only one of these bits will be set at any one time. The state transitions are caused by a foot switch, a proximity switch, and 3 different timers. One cycle of 5 states should take 10 seconds.