I can provide some insight into MN’s process for this.
It all really starts for new volunteers in the off-season. We have several off-season events, and will run training at any of them for interested volunteers. Our big focus is on an event called MRI here in the cities, but while it may be less structured, we still do it at other events (like Gitchi Gummi in Duluth) as needed.
For MRI, we provide dinner the evening before (Friday evening), and have 1-2 hour long sessions for some of the key positions - LRI, CSA, Ref, MC, etc. It’s a chance for those in those key positions to talk to (in my case) prospective Robot Inspectors and help them understand what’s expected, what they need to know, and everything the job entails.
We gather together the next morning and then they actually do the job. Inspectors go around in small groups (2-4 people, max) with an experienced inspector leading them to “inspect” robots. As there’s no required inspection at the event in order to play, this method doesn’t generally cause problems for teams, and a team always has the option to say no when we ask if we can walk through an inspection with them (Most say “Yes, let me get some underclassmen here to go through the experience!”). Other positions are similar - CSA’s go around looking at what teams are doing, MC’s/Game Announcers get to actually call a game on the field with immediate feedback from our veterans, Various field personnel roles get to experience what those roles are like and spend time with those key volunteers getting to know everything they need to.
During the season, it’s pretty much show up and do the job for most people. If you happened to make it to an off-season for training, you’re that much more prepared. If not, then we do what we can. For inspection, I have new inspectors “shadow” experienced inspectors through an inspection or two until they’re comfortable enough to do it themselves - I simply identify that as “expected” for new inspectors and let people self-identify from there, it’s not really a formal process.
Once we get through an event or the season, I generally talk with my fellow LRI’s in the state to see who they may have worked with that could be ready to become an LRI. We’re currently “full”, in that we have as many LRI’s as we can fit in the state, but I like to keep a pipeline of identified people that are ready to step up when needed. Once identified, we see if the person is interested, and then the following year at events we’ll have them shadow part-time, when the LRI is doing something they can learn from (Talking with the rookies in the morning, talking at the driver’s meeting, handling a significant issue, if appropriate, etc), the rest of the time they’re doing the same old job of inspecting robots. These individuals may also get some additional responsibilities, like getting a tough robot fixed up enough to pass inspection, or subbing in for the inspection manager for an hour or two to understand what that position is like.
For us, this process is overseen by our amazing VC, but is largely driven by the “department leads” for each area. Basically, she has a single LRI, and single FTA, a single Head Ref, etc that she uses to coordinate everything needed for that role. It means that I put in some energy organizing training and ensuring we have enough people where we need them in the off-season, and the other LRI’s in the state don’t need to worry about it (except when I bug them to help update a presentation or be at an off-season event). I took the role back in 2013-ish, and have since seen 4 new LRI’s come up in the state, and countless (Ok, I could count if I wanted to, I have a spreadsheet with info going back that far) RI’s get started. There are also several more individuals in the pipeline towards becoming and LRI, as we have room for them.
You can contrast this process to what we had when I became an LRI in 2012. I was asked if I was interested in 2011 by Jeff, said yes, and was told I would have a year of training before taking on the role (Which I thought was great, as I had no idea what would be involved!). The following year I was LRI for 2 events, as we were pretty desperate. And then Jeff went and moved to Wisconsin, leaving me with 4 events in the state and no one to help me run them 
I think having an established process like what we use here in MN is awesome. But I think it needs to be handled/run regionally, not from HQ. From HQ’s perspective, it’s all about the numbers - are there X number of robot inspectors, Y number of refs, etc. Regionally, however, it’s all about the people. We put so much effort into it because we know these people are going to be helping us staff the 4 events we run. Getting inspectors trained up and new LRI’s identified, trained, and “promoted” really is in my best interest - it make things so much easier for me during the season. There’s nothing better than going into an event with an inspector crew that is fully trained and staffed, and it’s so much less stressful being responsible for 1 regional instead of 2, even if they are 4-5 weeks apart. Having other trained LRI’s around makes my job easier as I have someone to talk through a situation with. Having someone that has some training for LRI, even if they don’t have the black vest yet, gives me an inspector I can rely on to help me create a successful event, even if I have to ask them to do something that isn’t strictly inspection related.