I don’t think there is a “right way” to call cues. For me it certainly depends on the situation that I am in. However, I can give you a couple of pointers and an example of my typical calling sequence.
1) When you say GO commit to it. An operator does not know what to do if the word is drawn out into multiple syllables. Additionally, an operator should be taking your GO on the G. The more lag there is in executing a cue the more difficult it becomes to call them in a consistent and timely manner.
2) When in doubt get a confirmation. Sometimes I have the luxury of being able to see if a light cue is running from the monitor attached to the console. When I can’t see a cue running or have doubts as to whether anything is changing on stage, I ask the operator. “We are in lights 34, correct?” “Lights 34 is running, correct?” I always make it a yes/no confirmation. I don’t need a story, just the answer.
3) I prefer to use Warning then Stand-by then GO as my sequence. Some people reverse the order of Warning and Stand-by. As long as your crew is clear on what is expected of them at each step, you could say Red, Yellow, and Green (not that I recommend this) with the same result. Clarity is more important than wording.
For me, I use warning when I know that a crew person may be otherwise occupied and need additional time to prepare for a cuing sequence. For example, if an ASM needs to move from one side of the stage to the other in order to cue an actors entrance I may give them a warning so that I know they are crossing. Or if a fly operator needs to move from the rail to a special piece of rigging I may give them a warning to that they have time to transition to a different location.
Stand-by is give about 15 seconds before the cue is called. I try to group stand-bys into cuing sequences so that I am not Calling a standby for one department while another is already standing-by. Sometimes this means that one department will be standing-by for a bit longer than another so that I call one group of stand-bys and then one group of GOs. Additionally, I always use the same order for departments when giving a group of stand-bys. I use: Lights, Sound, Deck, Rail, Projections, Effects. I there are no stand-bys for a particular department I leave them out of the call. This way operators always know what they are listening to and their stand-by is not thrown in as an after thought. Stand-bys are always something that I edit and refine during tech (and previews if I have any). I do not change them once I have opened.
For my GOs, I tend to pace myself in such a way that I have the same length wait between the cue number and GO every time. This will take some practice. I know some people mark in their book when they should start speaking the cue as well as the point at which the GO is called. You should do what works best for you. I try to be as consistent as possible so that my operators know what to expect. At no time should I be tricking them up with oddly times cues. Yes, sometimes a performer will jump a line or change the pace of their action in a way that effects your cuing. However, those moments should be the exceptions and not the rule.
So, ideally, when I call a cue sequence it sounds something like this:
Warning Rail on swing.
Standby Lights 7 through 9, Sound 15, and Rail on Swing.
Lights 8 and Sound 15..GO.
Lights 9 and Rail on Swing..GO.